Statistics Final Exam: MCQ Quiz!
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Appropriate graphical summary of the distribution of a categorical variable.
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Bar graph
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Box plot
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Stemplot
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Residual plot
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Scatter plot
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Do you think you could procure a good grade in the subject of statistics? Would you like to try it? In applying statistics to a question, it is a widespread practice to start a population or process to be studied. Statisticians compile data about the entire population, which is a procedure called a census. If you want to put your knowledge to the test, get ready to take this final statistics exam.
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- 2.
The standard deviation of Stats221 Final scores for a sample of 200 students was 10 points. An interpretation of this standard deviation is that the
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Typical distance of the Final scores from their mean was about 10 points
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The Finals scores tended to center at 10 points
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The range of Final scores is 10
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The lowest score is 10
Correct Answer
A. Typical distance of the Final scores from their mean was about 10 pointsExplanation
The standard deviation measures the average distance between each data point and the mean. In this case, since the standard deviation is 10 points, it means that on average, the Final scores deviated from their mean by about 10 points. This indicates that there is variability in the scores, with some scores being higher and some lower than the mean by approximately 10 points.Rate this question:
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- 3.
Which of the following data sets has the largest standard deviation?
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2, 3, 4, 5, 6,
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301, 304, 306, 308, 311
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350, 350, 350, 350, 350
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888.5, 888.6, 888.7, 888.9
Correct Answer
A. 301, 304, 306, 308, 311Explanation
The data set with the largest standard deviation is 301, 304, 306, 308, 311. This is because the standard deviation measures the amount of variation or dispersion in a set of data. In this data set, the numbers are spread out over a wider range compared to the other data sets, resulting in a larger standard deviation.Rate this question:
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- 4.
A researcher wants to know the average dating expenses for BYU single students. The researcher obtained a list of single students from the Records Office who live in the BYU dorms. From this list, 50 students are randomly selected. The 50 students are contacted by phone and the amount they spent on dates are recorded. The average dating expense of the 50 students is $35 with a standard deviation of $8. What is the population of interest?
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Average dating expenses of students
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All BYU Single students
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The 50 students selected
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All BYU students
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The number of single students who spends between $20 to $50 on date
Correct Answer
A. All BYU Single studentsExplanation
The population of interest in this study is all BYU single students. The researcher wants to know the average dating expenses for this specific group of students. The researcher obtained a list of single students from the Records Office who live in the BYU dorms and randomly selected 50 students from this list. The average dating expense of these 50 students is used as an estimate for the average dating expenses of all BYU single students.Rate this question:
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- 5.
An SRS of households shows a high positive correlation between the number of televisions in the household and the average IQ score of the people in the household. What is the most reasonable explanation for this observed correlation?
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A Type I error has occurred.
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Large households attract intelligent people.
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A mistake was made, since correlation should be negative.
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A lurking variable, such as higher socioeconomic condition, affects the association.
Correct Answer
A. A lurking variable, such as higher socioeconomic condition, affects the association.Explanation
A lurking variable, such as higher socioeconomic condition, affects the association. This means that there is another variable that is influencing both the number of televisions in the household and the average IQ score of the people in the household. It is likely that households with higher socioeconomic conditions have more resources to afford both more televisions and better education, leading to higher average IQ scores.Rate this question:
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- 6.
The shape of the sampling distribution of p-hat becomes approximately Normal as n gets large.
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True
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False
Correct Answer
A. TrueExplanation
As the sample size (n) gets larger, the shape of the sampling distribution of p-hat (the sample proportion) becomes approximately normal. This is due to the Central Limit Theorem, which states that for a large sample size, the sampling distribution of a sample statistic will be approximately normal regardless of the shape of the population distribution. Therefore, as n increases, the distribution of p-hat becomes more symmetric and bell-shaped, resembling a normal distribution.Rate this question:
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- 7.
A researcher wanted to estimate the average amount of money spent per semester on books by BYU students. An SRS of 100 BYU students were selected. They visited the addresses during the Summer term and had those students who were at home fill out a confidential questionnaire. This procedure is
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Likely to be biased because students are less likely to be enrolled during the Summer term.
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Unreliable because surveys are never as good as experiments.
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Unreliable because the sample size should be at least 500
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Unbiased because SRS was used to get the addresses.
Correct Answer
A. Likely to be biased because students are less likely to be enrolled during the Summer term.Explanation
Procedure is bias when some members of the population cannot be selected at all.Rate this question:
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- 8.
What does probability sampling allow us to do?
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Make inferences about population parameters
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Removes sampling variability
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Assess cause and effect relationship
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Exactly represents the population
Correct Answer
A. Make inferences about population parametersExplanation
Probability sampling allows us to make inferences about population parameters. This means that by using probability sampling methods, we can draw conclusions about the entire population based on the characteristics of the sample. This is because probability sampling ensures that every member of the population has an equal chance of being selected for the sample, reducing bias and increasing the representativeness of the sample. By making inferences about the sample, we can then generalize those findings to the larger population.Rate this question:
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- 9.
The Central limit theorem allows us
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Know exactly what the value of the sample mean will be.
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Specify the probability of obtaining each possible random sample of size n.
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Use the standard normal table to compute probabilities about sample means and sample proportions from a large random samples without knowing the distribution of the population.
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Determine whether the data are sampled from a population which is normally distributed.
Correct Answer
A. Use the standard normal table to compute probabilities about sample means and sample proportions from a large random samples without knowing the distribution of the population.Explanation
The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. This allows us to use the standard normal table to compute probabilities about sample means and sample proportions from large random samples without knowing the distribution of the population. This is because the standard normal distribution is well-known and its probabilities can be easily calculated.Rate this question:
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- 10.
Mean of the sampling distribution of p-hat.
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A
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B
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C
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D
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E
Correct Answer
A. DExplanation
The mean of the sampling distribution of p-hat represents the average value of all possible sample proportions that could be obtained from repeated sampling. It is an important measure in statistics as it provides information about the central tendency of the distribution and helps estimate the true population proportion.Rate this question:
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- 11.
Which research method can show a cause and effect relationship between the explanatory and response variables?
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A sample survey based on a simple random sample of single students.
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An observational study based on a carefully selected large SRS of single students.
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A comparative experiment where each single student is randomly assigned to one of two treatments
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A study using single students where the males are given the treatment and the females were given the placebo.
Correct Answer
A. A comparative experiment where each single student is randomly assigned to one of two treatmentsExplanation
A comparative experiment where each single student is randomly assigned to one of two treatments can show a cause and effect relationship between the explanatory and response variables. This is because in a comparative experiment, the researcher has control over the assignment of treatments, which allows for the manipulation of the explanatory variable. By randomly assigning each student to one of two treatments, any observed differences in the response variable can be attributed to the effect of the treatment. This helps establish a cause and effect relationship between the variables being studied.Rate this question:
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- 12.
A researcher wants to determine whether the time spent practicing free-throws after practice sessions can be used to predict the percentage free-throws in a game. What is the explanatory variable?
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Time spent practicing free-throws
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Number of practice sessions
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Percentage of free-throws in a game.
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Which method of shooting is used.
Correct Answer
A. Time spent practicing free-throwsExplanation
The explanatory variable in this scenario is the time spent practicing free-throws. The researcher wants to determine if the amount of time spent practicing free-throws after practice sessions can be used to predict the percentage of free-throws made in a game. Therefore, the researcher is interested in how the independent variable (time spent practicing free-throws) may have an effect on the dependent variable (percentage of free-throws made in a game).Rate this question:
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- 13.
A result that is statistically significant will also be practically significant.
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True
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False
Correct Answer
A. FalseExplanation
Statistical significance and practical significance are two different concepts. A result can be statistically significant, meaning that it is unlikely to have occurred by chance, but it may not have practical significance, meaning that it may not have a meaningful or substantial impact in the real world. Therefore, a result that is statistically significant may not necessarily be practically significant.Rate this question:
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- 14.
Testing multiple null hypotheses using the same data set increases the overall probability of making a type I error.
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True
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False
Correct Answer
A. TrueExplanation
When testing multiple null hypotheses using the same data set, the probability of making a type I error increases. This is because as more hypotheses are tested, the likelihood of at least one false positive result occurring by chance alone also increases. The more tests conducted, the higher the chance of falsely rejecting a true null hypothesis. Therefore, it is important to consider this increased risk of type I errors when conducting multiple hypothesis tests.Rate this question:
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- 15.
In practice, if the assumption of normality of the population is not met and n < 40 , confidence levels and P-values for t procedures are approximately correct provided:
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The The data has outliers.
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The data is very skewed.
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There are no outliers nor strong skewness in the data
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Cannot be determined.
Correct Answer
A. There are no outliers nor strong skewness in the dataExplanation
If the assumption of normality of the population is not met and the sample size is less than 40, confidence levels and P-values for t procedures are still approximately correct as long as there are no outliers or strong skewness in the data. This means that even if the data is not normally distributed, the t procedures can still be used to make accurate inferences about the population parameters as long as the data does not deviate significantly from normality due to outliers or strong skewness.Rate this question:
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- 16.
After a Church game, Jeremiah scored 40 points. His coach, who is a Statistics teacher, told him that the standardized score (z-score) for his points on the game, is 2.5. What is the best interpretation of this standardized score?
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Jeremiah’s score is only 2.5
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Only 2.5% of the players scored higher than Jeremiah
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Jeremiah’s scoring is 2.5 times the average scoring in the league
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Jeremiah’s scoring is 2.5 standard deviations above the average scoring in the league.
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Jeremiah’s scoring is 2.5 points above the average scoring in the league
Correct Answer
A. Jeremiah’s scoring is 2.5 standard deviations above the average scoring in the league.Explanation
Jeremiah's standardized score (z-score) of 2.5 indicates that his score is 2.5 standard deviations above the average scoring in the league. This means that his score is significantly higher than the average, demonstrating exceptional performance compared to other players.Rate this question:
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- 17.
Data on length of time to get married from the first date can be approximated by a Normal distribution with mean 3.5 months with a standard deviation of 0.3 month. Between what two values are the middle 95 of all lengths of time to get married from the first date?
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3.47 to 3.75
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2.9 to 4.1
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3.34 to 3.73
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3.43 to 3.75
Correct Answer
A. 2.9 to 4.1Explanation
The middle 95% of all lengths of time to get married from the first date can be found by calculating the range within which 95% of the data falls. In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. In this case, the mean is 3.5 months and the standard deviation is 0.3 months. Two standard deviations below the mean is 3.5 - (2 * 0.3) = 2.9 months, and two standard deviations above the mean is 3.5 + (2 * 0.3) = 4.1 months. Therefore, the middle 95% of all lengths of time to get married from the first date is between 2.9 and 4.1 months.Rate this question:
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- 18.
A FOX News report claims a margin of error 4% with 95% confidence when reporting the proportion of people who oppose the gay marriage initiative. Which of the following is the best interpretation of this margin of error?
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If the survey was conducted over and over again, 95% of the sample proportions will differ from the true proportion by no more than 4%.
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If the survey was conducted over and over again, 4% of the sample proportions will differ from the true proportion by no more than 95%.
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If the survey was conducted over and over again, 95% of the sample proportions will greater than the true proportion by more than 4%.
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FOX News is not Fair and Balance according to ABC News.
Correct Answer
A. If the survey was conducted over and over again, 95% of the sample proportions will differ from the true proportion by no more than 4%.Explanation
The given answer correctly interprets the margin of error. It states that if the survey is conducted multiple times, 95% of the sample proportions will differ from the true proportion by no more than 4%. This means that the reported proportion of people opposing the gay marriage initiative may vary within a range of 4% due to sampling variability. The answer accurately explains the concept of margin of error and its application in estimating population proportions.Rate this question:
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- 19.
Standard deviation of the sampling distribution of p-hat.
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A
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B
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C
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D
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E
Correct Answer
A. CExplanation
The standard deviation of the sampling distribution of p-hat represents the variability of the sample proportion. It measures how much the sample proportions from different samples are likely to vary from each other. A larger standard deviation indicates a greater spread of sample proportions, while a smaller standard deviation indicates a more consistent and reliable estimate of the population proportion. Therefore, option C is the correct answer.Rate this question:
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- 20.
For a particular set of data, the mean is less than the median. Which of the following statements is most consistent with this information?
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The distribution of the data is skewed to the right
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The distribution of the data is skewed to the left
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The distribution of the data is symmetric
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"mean is less than the median" does not give any information about the shape of the distribution.
Correct Answer
A. The distribution of the data is skewed to the leftExplanation
The fact that the mean is less than the median suggests that there are some smaller values in the dataset that are pulling the mean down. This indicates that the distribution is skewed to the left, as the tail of the distribution is on the left side.Rate this question:
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- 21.
The speed at which cars travel on I-15 has a normal distribution with a mean of 60 miles per hour and a standard deviation of 5 miles per hour. What is the probability that a randomly chosen car traveling on this highway is less than the 48 miles per hour?
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0.0082
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0.9918
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0.5
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None of the above.
Correct Answer
A. 0.0082Explanation
The probability that a randomly chosen car traveling on this highway is less than 48 miles per hour can be calculated using the standard normal distribution. We can convert the given value of 48 miles per hour into a z-score by subtracting the mean (60) and dividing by the standard deviation (5). This gives us a z-score of -2.4. Looking up this z-score in the standard normal distribution table, we find that the probability corresponding to this z-score is 0.0082. Therefore, the probability that a randomly chosen car traveling on this highway is less than 48 miles per hour is 0.0082.Rate this question:
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- 22.
BYU Creamery sells 16-ounce box of ice cream. The weight of the contents of a box of ice cream has a Normal distribution with mean=16 and a standard deviation of 1.1 ounces. AN SRS of 16 boxes of ice cream is to be selected and weighed and the average weight of the 16 boxes computed.If we did not know that weight of boxes of ice cream is Normally distributed, would it be appropriate to compute the approximate probability that x-bar is less than 15.3 ounces using the standard Normal distribution?
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NO, the sample size is too small to apply the Central Limit theorem.
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NO, the mean of the sampling distribution of x-bar is not equal to the population mean.
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YES, the sampling distribution of x-bar is approximately Normal.
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YES, the conditions are met to apply the Central Limit Theorem.
Correct Answer
A. NO, the sample size is too small to apply the Central Limit theorem.Explanation
The correct answer is NO, the sample size is too small to apply the Central Limit theorem. The Central Limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. However, for this question, the sample size is only 16, which is considered small. Therefore, the Central Limit theorem cannot be applied, and we cannot assume that the sampling distribution of the sample mean is approximately normal.Rate this question:
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- 23.
The BYU Admisnistration is planning a student opinion poll.. Initially they suggest s ample size of 500. But upon investigation it is discovered that this will give rise to a margin of error that is too small. What should the administration do to correct this?
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Decrease the sample size.
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Increase the sample size.
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Decrease the confidence level.
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Decrease the standard deviation.
Correct Answer
A. Decrease the sample size.Explanation
By decreasing the sample size, the administration will increase the margin of error. This means that the results of the student opinion poll will be less precise, but it will also allow for a larger margin of error, which is what the administration wants in this case. Increasing the sample size would actually decrease the margin of error, which is not desired. Decreasing the confidence level or the standard deviation would not address the issue of the margin of error being too small.Rate this question:
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- 24.
A simple random sample of full-time workers in the U.S. involved 817 full-time employees aged 40-50. They were asked to give their educational level (no high school, high school, some college, bachelor degree, some graduate education) and their level of financial satisfaction with their job (well satisfied, somewhat satisfied, not satisfied). The following MINITAB output is from the chi-square program. Rows are educational levels and columns are satisfaction levels: Ho: The proportions of people who are well satisfied financially are the same for all educational levels. Referring to the information above, is a chi-square analysis procedure appropriate for this set of data.
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No, because more than 20% of the components of the chi-square statistic are less than 5.
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No, because all expected counts are not whole numbers
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Yes, because all expected count are greater than 5
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Yes, because n is greater than 30
Correct Answer
A. Yes, because all expected count are greater than 5Explanation
A chi-square analysis procedure is appropriate for this set of data because all expected counts are greater than 5. This ensures that the assumptions for conducting a chi-square test are met, and the results can be considered reliable.Rate this question:
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- 25.
A simple random sample of full-time workers in the U.S. involved 817 full-time employees aged 40-50. They were asked to give their educational level (no high school, high school, some college, bachelor degree, some graduate education) and their level of financial satisfaction with their job (well satisfied, somewhat satisfied, not satisfied). The following MINITAB output is from the chi-square program. Rows are educational levels and columns are satisfaction levels: Ho: The proportions of people who are well satisfied financially are the same for all educational levels. Based on the analysis in question 1, we conclude at alpha=0.05 that
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The proportions of people who are well satisfied financially are not all equal for all educational levels
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The proportions of people who are well satisfied financially are the same for all educational levels
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There is no evidence of an association between educational level and financial satisfaction
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Cannot be determined
Correct Answer
A. The proportions of people who are well satisfied financially are not all equal for all educational levelsExplanation
The chi-square program was used to analyze the data and test the hypothesis that the proportions of people who are well satisfied financially are the same for all educational levels. The analysis concluded that at an alpha level of 0.05, the proportions of people who are well satisfied financially are not all equal for all educational levels. This means that there is evidence to suggest that there is a difference in the level of financial satisfaction among different educational levels.Rate this question:
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- 26.
If a result is statistically significant, then either the null hypothesis is false or a type I error was committed.
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True
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False
Correct Answer
A. TrueExplanation
If a result is statistically significant, it means that the observed data is unlikely to have occurred by chance alone. This suggests that there is evidence to reject the null hypothesis, which assumes that there is no relationship or difference between variables. Therefore, if a result is statistically significant, it is likely that the null hypothesis is false. Alternatively, there is a possibility that a type I error was committed, which means that the null hypothesis was incorrectly rejected.Rate this question:
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- 27.
Which of the following five statements about the correlation coefficient, r, is true?
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Changing the unit of measure for x changes the value of r.
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The unit measure on r is the same as the unit of measure on y.
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R is a useful measure of strength for any relationship between x and y.
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Interchanging x and y in the formula leaves the sign the same but changes the value of r.
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Where r is close to 1, there is a good evidence that x and y have strong positive linear relationship.
Correct Answer
A. Where r is close to 1, there is a good evidence that x and y have strong positive linear relationship.Explanation
The statement "Where r is close to 1, there is good evidence that x and y have a strong positive linear relationship" is true. The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables, x and y. When r is close to 1, it indicates a strong positive linear relationship, meaning that as x increases, y also tends to increase in a consistent manner. The closer r is to 1, the stronger the relationship between x and y.Rate this question:
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- 28.
We assume Ho is false whenever we perform a test of significance.
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True
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False
Correct Answer
A. FalseExplanation
The statement is false because we assume Ho (null hypothesis) is true whenever we perform a test of significance. The null hypothesis represents the default assumption or the status quo, and the purpose of the test is to gather evidence to either support or reject the null hypothesis. Therefore, we assume Ho is true until proven otherwise through the test.Rate this question:
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- 29.
The mean of the theoretical sampling distribution of x-bar is always equal to the population mean.
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True
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False
Correct Answer
A. TrueExplanation
The statement is true because the mean of the theoretical sampling distribution of x-bar is always equal to the population mean. This is known as the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean. Therefore, the mean of the theoretical sampling distribution of x-bar will always be equal to the population mean.Rate this question:
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- 30.
What is the primary purpose of a confidence interval for a population mean?
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To estimate the level of confidence.
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To specify a range for the measurements.
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To give a range of plausible values for the population mean.
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To determine if the population mean takes on a hypothesized value.
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To determine the difference between the sample mean and population mean.
Correct Answer
A. To give a range of plausible values for the population mean.Explanation
The primary purpose of a confidence interval for a population mean is to give a range of plausible values for the population mean. Confidence intervals provide a range of values within which the true population mean is likely to fall, based on the sample data. This range allows for uncertainty and variability in the estimate, giving researchers a sense of how precise their estimate is and the level of confidence they can have in it.Rate this question:
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- 31.
Coach Sloan claims that by using his method of shooting, basketball players can increase their scores by an average of 15 points. Wesley, a former basketball player is skeptical of this claim and wants to test the hypotheses: Ho: =15 versus Ha: <15 where represents the mean increase in scores of the population of all basketball players who have used the Sloan method. Wesley collects data from an SRS of 25 players who use the Sloan method. He finds that the sample mean increase in scores of these 25 players is 13 points with s=7. Assuming that the distribution of their scores is approximately normal, what is the p-value for this test?
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0.0830
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0.0228
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.10>p-value>.05
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.15>p-value>.10
Correct Answer
A. .10>p-value>.05Explanation
The p-value for a hypothesis test represents the probability of obtaining a sample mean as extreme as the one observed, assuming that the null hypothesis is true. In this case, the null hypothesis states that the mean increase in scores is equal to 15. The alternative hypothesis suggests that the mean increase is less than 15.
To find the p-value, we can use a one-sample t-test. With a sample mean of 13, a sample size of 25, and a sample standard deviation of 7, we can calculate the t-statistic. Using the t-distribution table or a statistical software, we find that the t-statistic corresponds to a p-value between .10 and .05. Therefore, the correct answer is ".10>p-value>.05".Rate this question:
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- 32.
When do we declare a result to be statistically significant?
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When the result has a large probability of occurring by chance.
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When the result has a small probability of occurring by chance.
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When it is practically significant.
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When the result is meaningful.
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When the result is consistent with our expectation.
Correct Answer
A. When the result has a small probability of occurring by chance.Explanation
We declare a result to be statistically significant when it has a small probability of occurring by chance. This means that the observed result is unlikely to have happened by random chance alone, suggesting that there is a real relationship or effect present. Statistical significance helps us determine if the observed data is reliable and can be generalized to a larger population. It provides evidence for the validity of our hypothesis and supports the idea that the observed result is not due to random variation.Rate this question:
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- 33.
Mean of the sampling distribution of x-bar.
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A
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B
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C
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D
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E
Correct Answer
A. EExplanation
The mean of the sampling distribution of x-bar is the same as the population mean. This means that, on average, the sample means will be equal to the population mean. This is because the sampling distribution of x-bar is created by taking multiple random samples from the population and calculating the mean of each sample. As the number of samples increases, the distribution of sample means will approach a normal distribution centered around the population mean. Therefore, the mean of the sampling distribution of x-bar is a good estimate of the population mean.Rate this question:
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- 34.
The sampling distribution of a statistic tells us
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The standard deviation of the population parameter.
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How the population parameter varies with repeated smples.
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Whether the sample is from a normal population provided the sample is SRS
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The possible values of the statistic and their frequencies from all possible samples.
Correct Answer
A. The possible values of the statistic and their frequencies from all possible samples.Explanation
The sampling distribution of a statistic tells us the possible values of the statistic and their frequencies from all possible samples. This means that it provides information about the range of values that the statistic can take and how often each value occurs when multiple samples are taken from the population. It helps us understand the variability and distribution of the statistic across different samples, which is important for making inferences about the population based on the sample.Rate this question:
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- 35.
A simple random sample of full-time workers in the U.S. involved 817 full-time employees aged 40-50. They were asked to give their educational level (no high school, high school, some college, bachelor degree, some graduate education) and their level of financial satisfaction with their job (well satisfied, somewhat satisfied, not satisfied). The following MINITAB output is from the chi-square program. Rows are educational levels and columns are satisfaction levels:Ho: The proportions of people who are well satisfied financially are the same for all educational levels.Assuming Ho is true, what is the expected count for people who completed high school and not financially satisfied.
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85.4
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95.6
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100.5
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104.6
Correct Answer
A. 104.6Explanation
The expected count for people who completed high school and are not financially satisfied is 104.6. This is calculated based on the assumption that the proportions of people who are well satisfied financially are the same for all educational levels. The chi-square test is used to determine if there is a significant difference between the observed and expected counts, and in this case, the expected count for this particular category is 104.6.Rate this question:
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- 36.
Experiments was conducted on how long in months it takes dating single students get married.For one particular Ward, the mean time is 12 months. Drew thinks that getting a 2% extra credits in Stats class for dating cause these students to marry faster. He plans to measure how long it takes for 20 dating students to get married with the extra credits as a stimulus. What are the appropriate Ho and Ha?a. Ho: µ = 20 versus Ha: µ < 20b. Ho: µ = 12 versus Ha: µ < 12c. Ho: µ = 12 versus Ha: µ > 12 d. Ho: µ = 12 versus Ha: µ NE 12e. None of the above.
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A
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B
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C
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D
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E
Correct Answer
A. BExplanation
The appropriate Ho and Ha for this experiment are Ho: µ = 12 versus Ha: µ < 12. This is because the null hypothesis (Ho) states that there is no difference in the mean time it takes for dating students to get married with or without the extra credits. The alternative hypothesis (Ha) suggests that the mean time for students with the extra credits is less than 12 months, indicating that the extra credits may cause them to marry faster.Rate this question:
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- 37.
Standard error of x-bar.
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A
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B
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C
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D
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E
Correct Answer
A. BExplanation
The standard error of x-bar refers to the standard deviation of the sample mean. It measures the variability or dispersion of the sample means from the population mean. A smaller standard error indicates that the sample means are closer to the population mean, suggesting greater precision and accuracy in estimating the population mean. Therefore, option B is the correct answer as it accurately defines the standard error of x-bar.Rate this question:
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- 38.
The following histrogram is a distribution of Religiosity of 226 people. What percent of these people had Religiosity in the 56-60 Religiosity range?
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31%
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41%
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51%
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61%
Correct Answer
A. 31%Explanation
The correct answer is 31%. This means that out of the 226 people surveyed, 31% of them had a religiosity level in the range of 56-60.Rate this question:
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- 39.
Given the figure below: If basketballs X, Y, and Z are added to the group of five balls at the left, how will the standard deviation of the volume of the new 8 balls compare with the standard deviation of the volume of the original set of 5? The standard deviation of the volume of the new set of 8 balls will be _________ the standard deviation of the volume of the original 5 balls. Fill in the blank.
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Will be about the same
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Will be greater than
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Will be less than
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Cannot be compared to
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Cannot be computed since the balls are such different sizes
Correct Answer
A. Will be greater thanExplanation
When basketballs X, Y, and Z are added to the group of five balls, the new set of eight balls will have more variability in volume compared to the original set of five balls. This is because the addition of the three basketballs introduces more diversity in sizes, resulting in a larger range of volumes. As a result, the standard deviation of the volume of the new set of eight balls will be greater than the standard deviation of the volume of the original five balls.Rate this question:
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- 40.
The speed at which cars travel on I-15 has a normal distribution with a mean of 60 miles per hour and a standard deviation of 5 miles per hour. What is the probability that a randomly chosen car traveling on this highway has a speed between 75 and 63 mph?
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.2729
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.9918
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.50
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None of the above.
Correct Answer
A. .2729Explanation
The probability that a randomly chosen car traveling on this highway has a speed between 75 and 63 mph can be calculated by finding the area under the normal distribution curve between these two speeds. This can be done by calculating the z-scores for both speeds using the formula z = (x - μ) / σ, where x is the speed, μ is the mean, and σ is the standard deviation. Then, using a z-table or a calculator, we can find the probability associated with these z-scores. The correct answer of .2729 represents the probability that falls within this range.Rate this question:
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- 41.
In hypothesis testing, what does the symbol αdenote?
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The power of the test.
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The probability that Ho is true.
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The probability of Type II error.
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The probability of Type I error.
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The probability of rejecting a false null hypothesis.
Correct Answer
A. The probability of Type I error.Explanation
The symbol α in hypothesis testing represents the probability of Type I error. Type I error occurs when the null hypothesis (Ho) is rejected, even though it is true. In other words, it is the probability of incorrectly rejecting a true null hypothesis.Rate this question:
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- 42.
The following data are from a study of the relationship between Stats221 Test3 scores and the Final scores. The response variable is Final scores (FS) and the explanatory variable is Test3 scores (TS). TS 90 81 75 94 65 FS 88 84 78 93 60 The slope of the least-squares line, b, is equal to 1.4. Which statement is the best interpretation of b?
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On the average, FS increases by about 1.4 units when the Test3 score increases by 1 unit
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On the average, TS increases by about 1.4 units when the Final score increases by 1 unit
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The correlation between FS and TS is 1.4
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The proportion of variation in FS that is explained by the regression model is 1.4
Correct Answer
A. On the average, FS increases by about 1.4 units when the Test3 score increases by 1 unitExplanation
The slope of the least-squares line represents the change in the response variable (Final scores) for every 1 unit increase in the explanatory variable (Test3 scores). In this case, the slope is 1.4, which means that, on average, the Final scores increase by about 1.4 units when the Test3 scores increase by 1 unit.Rate this question:
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- 43.
Which of the following is the conditional distribution for college Majors for students whose last Math class taken was College Algebra?
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A
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B
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C
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D
Correct Answer
A. DExplanation
The conditional distribution for college Majors for students whose last Math class taken was College Algebra is represented by option D.Rate this question:
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- 44.
The BYU records office found that 80% of all students who took Stats221 at the BYU Salt Lake Center worked full-time. The value 80% is a
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Mean
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Statistic
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Parameter
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Margin of error
Correct Answer
A. ParameterExplanation
The value 80% is a parameter. In statistics, a parameter is a numerical value that describes a population characteristic. In this case, the population is all students who took Stats221 at the BYU Salt Lake Center. The 80% represents the proportion of these students who worked full-time. Since it is based on data from the entire population, it is considered a parameter rather than a statistic, which would be based on a sample of the population.Rate this question:
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- 45.
A simple random sample of full-time workers in the U.S. involved 817 full-time employees aged 40-50. They were asked to give their educational level (no high school, high school, some college, bachelor degree, some graduate education) and their level of financial satisfaction with their job (well satisfied, somewhat satisfied, not satisfied). The following MINITAB output is from the chi-square program. Rows are educational levels and columns are satisfaction levels: Ho: The proportions of people who are well satisfied financially are the same for all educational levels. Referring to question above, what are the degrees of freedom for the chi-square statistic?
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2
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4
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6
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8
Correct Answer
A. 8Explanation
The degrees of freedom for the chi-square statistic in this case would be 8. This is because the degrees of freedom for a chi-square test is calculated by subtracting 1 from the number of categories in each variable and then multiplying those values together. In this case, there are 5 categories for educational levels (no high school, high school, some college, bachelor degree, some graduate education) and 3 categories for satisfaction levels (well satisfied, somewhat satisfied, not satisfied), so the degrees of freedom would be (5-1) * (3-1) = 8.Rate this question:
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- 46.
Why do we do randomization in an experiment?
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To do double blind experimetn.
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To increase accuracy of the results.
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To make the experiment realistic.
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To help avoid selection bias.
Correct Answer
A. To help avoid selection bias.Explanation
Randomization in an experiment is done to help avoid selection bias. Selection bias occurs when the participants or subjects in the experiment are not representative of the target population, leading to biased results. By randomly assigning participants to different groups or treatments, randomization ensures that the groups are similar in terms of their characteristics and reduces the likelihood of any systematic differences. This helps to minimize the impact of selection bias and increases the validity and generalizability of the results obtained from the experiment.Rate this question:
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- 47.
Following is a five-number summary of the number of dates, before getting married, of 100 BYU students. Min Q1 Median Q3 Max 10 40 80 100 500 about 25% of the students participated in more than ______________________ dates before getting married.
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10
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40
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80
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100
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500
Correct Answer
A. 100Explanation
About 25% of the students participated in more than 100 dates before getting married. This can be determined by looking at the Q1 (the first quartile) value, which represents the 25th percentile. Since the Q1 value is 40, it means that 25% of the students had less than or equal to 40 dates. Therefore, the remaining 75% of the students had more than 40 dates, indicating that about 25% of the students participated in more than 100 dates.Rate this question:
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- 48.
Explain the meaning of “95% confidence interval “.
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There is a 95% probability that the interval contains x-bar.
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The interval contains the value of x-bar with 95% confidence.
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95% of the data is contained in the interval.
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For 95% of all possible samples, the procedure used to obtain the confidence interval provides an interval containing the population mean
Correct Answer
A. For 95% of all possible samples, the procedure used to obtain the confidence interval provides an interval containing the population meanExplanation
The correct answer explains that a 95% confidence interval means that for 95% of all possible samples, the procedure used to obtain the confidence interval will provide an interval that contains the population mean. This means that if the same procedure is repeated multiple times, 95% of the intervals obtained will contain the true population mean. It is a measure of the level of confidence we have in the accuracy of the interval estimate.Rate this question:
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- 49.
The following histrogram is a distribution of Religiosity of 226 people. How many of these people had Religiosity less than 34 Religiosity range?
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6
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8
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12
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20
Correct Answer
A. 12Explanation
The histogram shows the distribution of religiosity among 226 people. The numbers on the y-axis represent the frequency of people falling into each religiosity range. The x-axis represents the different religiosity ranges. The answer is 12 because the histogram shows that there are 12 people who had a religiosity less than the 34 religiosity range.Rate this question:
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