Probability Sample Test

1. AN event has probability 0.0. Which one of the following statements best describes this event in along sequence of trials?

This event is extremely likely and will occur almost all the time.

This event is likely and will occur more often than not in the long run.

This event is likely; however it is more likely to NOT occur than to occur.

This event is very unlikely, but it will occur once in a while.

This event is impossible. It can never occur.

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

Explanation

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

2. AN event has probability 0.95. Which one of the following statements best describes this event in along sequence of trials?

This event is certain. It will definitely occur on every trial.

This event is extremely likely and will occur almost all the time.

This event is likely and will occur more often than not in the long run.

This event is likely; however it is more likely to NOT occur than to occur.

This event is very unlikely, but it will occur once in a while.

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

Explanation

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

3. AN event has probability 1.0. Which one of the following statements best describes this event in along sequence of trials?

This event is certain. It will definitely occur on every trial.

This event is extremely likely and will occur almost all the time.

This event is likely and will occur more often than not in the long run.

This event is likely; however it is more likely to NOT occur than to occur.

This event is very unlikely, but it will occur once in a while.

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

Explanation

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

4. AN event has probability 0.35. Which one of the following statements best describes this event in along sequence of trials?

This event is certain. It will definitely occur on every trial.

This event is extremely likely and will occur almost all the time.

This event is likely and will occur more often than not in the long run.

This event is likely; however it is more likely to NOT occur than to occur.

This event will occur half of the time in the long run

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

Explanation

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

5. AN event has probability 0.05. Which one of the following statements best describes this event in along sequence of trials?

This event is extremely likely and will occur almost all the time.

This event is likely and will occur more often than not in the long run.

This event is likely; however it is more likely to NOT occur than to occur.

This event is very unlikely, but it will occur once in a while.

This event is impossible. It can never occur.

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

Explanation

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

6. Use the counts of the following table to answer the following questions:

Of the lawyers, what percent are Asians?

18.18%

15.38%

27.08%

30.76%

20/130=15.38

Explanation

20/130=15.38

7. A study reported a correlation of r=0.75 between political party and affiliation and his or her GPA. Which one of the following is an appropriate conclusion about the report?

Republicans have higher GPA than Democrats.

Republicans have lower GPA than Democrats.

A calculation error was made - correlation must be negative.

This is incorrect because r makes no sense in this context.

correlation is for two quantitative variables. No categorical variables.

Explanation

correlation is for two quantitative variables. No categorical variables.

8. What does Central Limit Theorem allow us to do?

Calculate probabilities of sample mean from a large random sample taken from a non-Normal population.

Determine whether the data are sampled from a population which is Normally distributed.

Specify the probability of obtaining each possible random sample of size n.

Know exactly what the value of the sample mean will be.

The Central Limit Theorem allows us to calculate probabilities of sample mean from a large random sample taken from a non-Normal population.

Explanation

The Central Limit Theorem allows us to calculate probabilities of sample mean from a large random sample taken from a non-Normal population.

9. The histogram below represents the distribution of a population. Suppose a sampling distribution of

is constructed from samples of size 60 from this population. Which one of the following figures best represents the sampling distribution?

A

B

C

D

The sampling distribution is Normal with less spread and taller regardless of size when the population is already Normal.

Explanation

The sampling distribution is Normal with less spread and taller regardless of size when the population is already Normal.

10. Use the counts of the following table to answer the following questions:

Of the Asians, what percent are lawyers?

45.45%

18.18%

10.42%

81.81%

20/110=18.18

Explanation

20/110=18.18

11. In order to apply the Central Limit Theorem when sampling from a non-Normal population, which one of the following states the necessary conditions?

The population must not be skewed.

The population distribution from which the data are sampled must be Normal.

A large simple random sample must be taken.

The data must have a bell-shaped distribution.

When sampling from a non-Normal population, a large (n>=30) simple random sample must be taken for the Central Limit to hold that the shape of the sampling distribution is Normal.

Explanation

When sampling from a non-Normal population, a large (n>=30) simple random sample must be taken for the Central Limit to hold that the shape of the sampling distribution is Normal.

12. Andy, Samantha, Britt, and Christine have each taken a random sample of single students from BYU to estimate the variability in amount spent on dates this semester. Andy asked 15 people, Samantha 25, Britt 40, and Christine 50. Whose sample standard deviation probably differs the least from the population standard deviation?

Andy

Samantha

Britt

Christine

From the law of large numbers, the sample stdev will be closer to the population stdev the larger the sample size, just like the sample mean will be closer to the population mean as the sample size increases.
Please note that we are not talking about the standard deviation of the sampling distribution.

Explanation

From the law of large numbers, the sample stdev will be closer to the population stdev the larger the sample size, just like the sample mean will be closer to the population mean as the sample size increases.
Please note that we are not talking about the standard deviation of the sampling distribution.

13. Home prices follow an extremely right skewed distribution with mean $200k and a standard deviation of $30k. If we select an SRS of 16 homes, can we use the standard Normal table to validly calculate the probability that their average home price is is greater than $250k?

No, because the population standard deviation is not known.

No, because the Central Limit Theorem does not apply.

Yes, because of the sampling distribution of sample means is Normal.

Yes, because of the Law of Large numbers.

When sampling from a non-Normal population, a large (n>=30) simple random sample must be taken for the Central Limit to hold that the shape of the sampling distribution is Normal.

Explanation

When sampling from a non-Normal population, a large (n>=30) simple random sample must be taken for the Central Limit to hold that the shape of the sampling distribution is Normal.

14. Consider the theoretical sampling distribution of sample means based on samples of size 50 from a uniform (flat) population where the population mean=70 and population standard deviation =10.

The shape of the theoretical sampling distribution of sample means is

Approximately Normal.

Right skewed.

Left skewed.

Flat or uniform.

If n>=30 and the population in non-normal, the shape of the sampling distribution for x-bar is normal.

Explanation

If n>=30 and the population in non-normal, the shape of the sampling distribution for x-bar is normal.

15. Assuming the scales on the x and y axis are the same for all graphs, which of the following shows a weak positive relationship.

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A

B

C

D

The more scattered the points from an imaginary line, the weaker the correlation.

Explanation

The more scattered the points from an imaginary line, the weaker the correlation.

16. Select the appropriate symbol below for the standard deviation of observations in a population.

A

B

C

D

E

The symbol for the standard deviation of observations in a population is represented by the letter D.

Explanation

The symbol for the standard deviation of observations in a population is represented by the letter D.

17. The histogram below represents the distribution of a population. Suppose a sampling distribution of

is constructed from samples of size 60 from this population. Which one of the following figures best represents the sampling distribution?

A

B

C

D

The sampling distribution is Normal with less spread and taller when n>=30.

Explanation

The sampling distribution is Normal with less spread and taller when n>=30.

18. Select the appropriate symbol below for the mean of observations in a sample.

A

B

C

D

E

The symbol "A" represents the mean of observations in a sample. The mean is a measure of central tendency that represents the average value of a set of observations. It is calculated by summing up all the observations and dividing by the total number of observations in the sample. The symbol "A" is commonly used to denote the mean in statistical notation.

Explanation

The symbol "A" represents the mean of observations in a sample. The mean is a measure of central tendency that represents the average value of a set of observations. It is calculated by summing up all the observations and dividing by the total number of observations in the sample. The symbol "A" is commonly used to denote the mean in statistical notation.

19. Use the counts of the following table to answer the following questions:

What is the marginal percent of respondents who are lawyers?

18.18%

15.38%

42.86%

30%

27.08%

130/480=27.08

Explanation

130/480=27.08

20. Which one of the following concepts says that if sample mean is based on a large simple random sample from a non-normal population, we can calculate approximate probabilities on sample mean using the standard Normal table?

The Law of Large Numbers.

The Central Limit Theorem.

The principle of least squares.

The sampling distribution of the mean.

There is no such result.

The Central Limit theorem states that if sample mean is based on a large simple random sample from a non-normal population, we can calculate approximate probabilities on sample mean using the standard Normal table

Explanation

The Central Limit theorem states that if sample mean is based on a large simple random sample from a non-normal population, we can calculate approximate probabilities on sample mean using the standard Normal table

21. Use the counts of the following table to answer the following questions:

Which of the following is the conditional distribution for Professions for those whose ethnicity is Asian?

A

B

C

D

50/110=45.4; 20/110=18.2; 10/110=9.1; 30/110=27.3

Explanation

50/110=45.4; 20/110=18.2; 10/110=9.1; 30/110=27.3

22. Which one of the following control charts show a process that is in statistical control?

A

B

C

D

Out of control charts when points are outside the UCL or LCL, and 9 consecutive points below or above the mean.

Explanation

Out of control charts when points are outside the UCL or LCL, and 9 consecutive points below or above the mean.

23. Consider these plots: the plot on the left is a scatterplot and the plot on the right is the corresponding residual plot from fitting a regression line. On the basis of these plots, is fitting the data with least-squares regression appropriate? Why or why not?

No, because the relationship between X and Y is non-linear.

No, because Y has more spread for larger value of X.

No, because there is no relationship between X and Y.

Yes, because X and Y has a linear relationship.

Yes, because there is a relationship between X and Y.

fitting the data with least-squares regression is appropriate when the scatter plot shows a linear pattern.

Explanation

fitting the data with least-squares regression is appropriate when the scatter plot shows a linear pattern.

24. Fill in the blank: If sampling distributions of sample means are examined for samples of size 9, 16, 25, and 36 from a non-Normal population, you will notice that as n increases in size, the shape of the sampling distribution appears more like that of the _____________________.

Sample distribution

Uniform distribution

Population distribution

Normal distribution.

from a non-Normal population, you will notice that as n increases in size, the shape of the sampling distribution appears more like that of the Normal distribution.

Explanation

from a non-Normal population, you will notice that as n increases in size, the shape of the sampling distribution appears more like that of the Normal distribution.

25. Imagine that we have a population that is skewed to the right. This population has a mean of 70 and a standard deviation of 10. Using a simulation program, Jesse simulated drawing all possible samples of size 8 from the population. He then plotted the means for each of the samples that he drew. Preston simulated drawing all possible samples of size 50, and he also plotted the means for each of the samples that he drew.

How would the shape of Jesse's distribution of sample means differ from the shape of Preston's distribution of sample means?

Both would be approximately Normal.

Jesse's distribution would be closer to the shape of the population whereas Preston's distribution would be closer to Normal.

Jesse's distribution would be closer to a Normal shape than Preston's distribution.

They would both have approximately the same shape and would resemble the shape of the population distribution.

The larger the sample size (n>=30) the shape of the distribution of sample means is Normal.

Explanation

The larger the sample size (n>=30) the shape of the distribution of sample means is Normal.

26. AN event has probability 0.5. Which one of the following statements best describes this event in along sequence of trials?

This event is certain. It will definitely occur on every trial.

This event is extremely likely and will occur almost all the time.

This event is likely and will occur more often than not in the long run.

This event is likely; however it is more likely to NOT occur than to occur.

This event will occur half of the time in the long run

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

Explanation

1. Prob=1, this event is certain. It will definitely occur on every trial.
2. .8 3. .5 4. Prob=.5, this event is likely to occur half of the time.
5. .3 6. 0 7. Prob=0, this event is impossible. It can never occur.

27. The data in the table below represent distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at month. The line in the scatterplot is the least squares line:

where

y-hat is the predicted length of time and x=distance of shipment, in miles.

Seattle is 2984 shipping miles from Cleveland, Ohio. Should you use this least squares equation to predict the shipping days?

No, because we do not know whether the deviation will be positive or negative.

No, because Seattle is much farther away than any other observed city in the data set.

Yes, because the predicted value is reasonable.

Yes, because the increase in shipping days is the same for each shipping mile.

Do not use the least squares equation to predict y when x is outside the range of the data. This is called extrapolation.

Explanation

Do not use the least squares equation to predict y when x is outside the range of the data. This is called extrapolation.

28. The scatter plot below depicts the relationship between calories and sodium content of several brands of meat hotdogs. The least squares line has been drawn on the plot. What does the point labeled A in the scatterplot indicate?

The point labeled A does not have a residual.

The point labeled A has a positive residual.

The point labeled A has a negative residual.

The point labeled A is not an outlier.

Points above the line have positive residuals.
Points below the line have negative residuals.

Explanation

Points above the line have positive residuals.
Points below the line have negative residuals.

29. The data in the table below represent distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at month. The line in the scatterplot is the least squares line:

where

y-hat is the predicted length of time and x=distance of shipment, in miles.

The distance of a package to be shipped is 500 miles. What is the predicted delivery time in days?

6.9 days

.02 day

3.1 days

Cannot be computed.

y=-6.9+.02(500) = 3.1

Explanation

y=-6.9+.02(500) = 3.1

30. Select the appropriate symbol below for the mean of observations in a population.

A

B

C

D

E

The symbol B is the appropriate symbol for the mean of observations in a population. The mean is often represented by the symbol μ (pronounced "mu"), which is similar in appearance to the letter B. Therefore, B is the correct symbol to represent the mean of observations in a population.

Explanation

The symbol B is the appropriate symbol for the mean of observations in a population. The mean is often represented by the symbol μ (pronounced "mu"), which is similar in appearance to the letter B. Therefore, B is the correct symbol to represent the mean of observations in a population.

31. A study was done of the accuracy of three-point shooting using Doria’s method and the traditional method. Dan Bentley took sixty shots using Doria’s method and 50 shots using the traditional method. The results are in the following table:

Based on the information above, which of the following best describes Dan’s three-point shooting?

Dan shoots better using Doria method.

Dan shoots better using Traditional method.

There is no association between Dan’s shooting percentage and method of shooting.

There is a strong association between Dan’s shooting percentage and method of shooting.

36/60=.6; 30/50=.6; 66/110=.6
If the conditional and marginal percentages are equal then there is NO association between the two categorical variables.

Explanation

36/60=.6; 30/50=.6; 66/110=.6
If the conditional and marginal percentages are equal then there is NO association between the two categorical variables.

32. How does the correlation coefficient r for the data in Plot A compares with the correlation coefficient for the data in Plot B?

R in Plot A is less than r in Plot B.

R in Plot A is greater than r in Plot B.

R in Plot A is equal to r in Plot B.

R in Plot A is not comparable with r in Plot B.

Not enough information exists to compare the two r's.

Outliers lower the correlation.

Explanation

Outliers lower the correlation.

33. A survey conducted by the Statistics Department to assess the study habits of the Stats221 students and obtained data from a sample of 1000 Stats221 students. The average number of hours per week studying for Stats221 class was found to be 15 with a standard deviation of 5. Is 15 a parameter or a statistic? Why?

A parameter because the average is for all Stats221 students.

A parameter because is the average for all Stats221 students at BYU.

A statistic because it summarizes the results of the entire population of Stats221 students at BYU.

A statistic because it summarizes the results of this sample of 1000 Stats221 students.

Parameter refers to population mean or population standard deviation or population proportion.
Statistics refers to sample mean or sample standard deviation or sample proportion.

Explanation

Parameter refers to population mean or population standard deviation or population proportion.
Statistics refers to sample mean or sample standard deviation or sample proportion.

34. Cost of dates in a semester of single students at BYU are Normally distributed with mean $380. A study is being planned to determine whether cost of dates in a semester for single students who are returned missionaries differ from the BYU mean. Proposed sample #1 has a sample size of 50 and proposed sample #2 has a sample size of 25. Which proposed sample is more likely to have an unusually high sample mean (i.e., a sample mean exceeding $500 on dates)?

Proposal sample #1

Proposal sample #2

Both proposed samples have equal chance of having an unusually high sample mean.

The smaller the sample size, the larger the stdev of x-bar.
The larger the sample size, the smaller the stdev of x-bar.
stdev of x-bar=sigma/sqrt(n)

Explanation

The smaller the sample size, the larger the stdev of x-bar.
The larger the sample size, the smaller the stdev of x-bar.
stdev of x-bar=sigma/sqrt(n)

35. Andy, Samantha, Britt, and Christine have each taken a random sample of single students from BYU to estimate the variability in amount spent on dates this semester. Andy asked 15 people, Samantha 25, Britt 40, and Christine 50. Whose sample standard deviation probably differs most from the population standard deviation?

Andy

Samantha

Britt

Christine

From the law of large numbers, the sample stdev will be closer to the population stdev the larger the sample size, just like the sample mean will be closer to the population mean as the sample size increases.

Explanation

From the law of large numbers, the sample stdev will be closer to the population stdev the larger the sample size, just like the sample mean will be closer to the population mean as the sample size increases.

36. Referring to the scatterplot below, what is the best guess for the value of the correlation coefficient r between the explanatory and response variables?

0.85

0.45

-0.85

-0.45

0.35

This has a negative correlation.

Explanation

This has a negative correlation.

37. Consider the theoretical sampling distribution of sample means based on samples of size 50 from a uniform (flat) population where the population mean=70 and population standard deviation =10.

The mean of the theoretical sampling distribution of sample means

Is greater than 70 because of the skewness.

Is close to but not equal to 70.

Is exactly equal to 70.

Cannot be determined.

The mean of all the sample means=the population mean.

Explanation

The mean of all the sample means=the population mean.

38. In the Casino Royale movie, James Bond played a card game called Baccarat. He wins by playing in a specified manner. Which of the following is true about the probability of winning the game?

It can be computed from the number of ways the 52 cards can be dealt.

It is impossible to compute.

It is approximated by playing lots of times and dividing the number of times you win by the number of times you play.

It is ,007 because this is Bond's number.

Probability is the number of success divided by the total possibilities.

Explanation

Probability is the number of success divided by the total possibilities.

39. The histogram below represents the distribution of a population. Suppose a sampling distribution of

is constructed from samples of size 60 from this population. Which one of the following figures best represents the sampling distribution?

A

B

C

D

The sampling distribution is Normal with less spread and taller when n>=30.

Explanation

The sampling distribution is Normal with less spread and taller when n>=30.

40. Select the appropriate symbol below for the standard deviation of the sampling distribution of sample means.

A

B

C

D

E

The symbol "E" represents the standard deviation of the sampling distribution of sample means. This symbol is commonly used to denote the standard error, which is the standard deviation of the sample means. The standard error measures the variability of the sample means around the population mean and is an important concept in inferential statistics. Therefore, the correct answer is E.

Explanation

The symbol "E" represents the standard deviation of the sampling distribution of sample means. This symbol is commonly used to denote the standard error, which is the standard deviation of the sample means. The standard error measures the variability of the sample means around the population mean and is an important concept in inferential statistics. Therefore, the correct answer is E.

41. Consider the statement " The survey finds differences between Asians and Caucasians over professions. Just 7% of the Caucasians say that they are engineers; by contrast, more than 45% of the Asians say that they are engineers." Which of the following agrees with this statement:

There is a curved relationship between ethnicity and profession.

There is a linear relationship between ethnicity and profession.

There is an association between ethnicity and profession.

There is no association between ethnicity and profession.

When the percentages are not equal then there is association between the two categorical variables.

Explanation

When the percentages are not equal then there is association between the two categorical variables.

42. Consider these plots: the plot on the left is a scatterplot and the plot on the right is the corresponding residual plot from fitting a regression line. On the basis of these plots, is fitting the data with least-squares regression appropriate? Why or why not?

No, because the relationship between X and Y is non-linear.

No, because Y has more spread for larger value of X.

No, because there is no relationship between X and Y.

Yes, because X and Y has a linear relationship.

Yes, because there is a relationship between X and Y.

fitting the data with least-squares regression is NOT appropriate if the scatter plot shows non-linear pattern.

Explanation

fitting the data with least-squares regression is NOT appropriate if the scatter plot shows non-linear pattern.

43. Consider the theretical smpling distribution of sample means based on samples of size 50 from a uniform (flat) population where the population mean=70 and population standard deviation =10.

The standard deviation of the theoretical sampling distribution of sample means

Is less than 10.

Is exactly equal to 10.

Is greater than 10.

Cannot be determined.

stdev of x-bar=sigma/sqrt(n)=10/sqrt(50)=1.41

Explanation

stdev of x-bar=sigma/sqrt(n)=10/sqrt(50)=1.41

44. The data in the table below represent distance a shipment must travel and the length of time, in days, it takes the shipment to arrive . The line in the scatterplot is the least squares line:

where

y-hat is the predicted length of time and x=distance of shipment, in miles.

Interpret the slope of the regression line in context.

For each additional mile, time in days to deliver the shipment increases by .02 day on average.

For each additional mile, time in days to deliver the shipment increases by 6.9 days on average

For each additional day, there is a 0.02 miles a shipment traveled on the average.

For each additional day, there is a 6.9 miles a shipment traveled on the average.

slope is the average increase/decrease in y per one unit change in x.

Explanation

slope is the average increase/decrease in y per one unit change in x.

45. Researchers recorded facts about 100 dates, including cost spent on date and number of hugs they gave each other on a date. The linear model relating cost spend on date and the number of hugs the couple gave each other is predicted number of hugs = 3.5 + 1.5cost. Based only on the given information, what can be said about the correlation between cost spend on date and the number of hugs the couple gave each other?

The correlation is 0.

The correlation is 1.5

The correlation 3.5

The correlation is positive, but we cannot say what the exact value is.

It is impossible to say anything about the correlation from the information given.

The slope has the same sign as the correlation.

Explanation

The slope has the same sign as the correlation.

46. Select the appropriate symbol below for the standard deviation of observations in a sample.

A

B

C

D

E

The symbol "C" represents the appropriate symbol for the standard deviation of observations in a sample. The standard deviation is a measure of the dispersion or variability of the data points in a sample. It is commonly represented by the Greek letter sigma (σ) in statistics. Therefore, option C is the correct symbol for the standard deviation.

Explanation

The symbol "C" represents the appropriate symbol for the standard deviation of observations in a sample. The standard deviation is a measure of the dispersion or variability of the data points in a sample. It is commonly represented by the Greek letter sigma (σ) in statistics. Therefore, option C is the correct symbol for the standard deviation.

47. The mean GPA of BYU Salt Lake Center students was 3.5, with a standard deviation of 0.8. The distribution was skewed to right. Suppose you took 1,000 simple random samples of 64 students, and computed the mean GPA for each sample. Between what two values would you expect approximately the 95% of the mean GPA of the samples to be?

A. (3.4, 3.9)

B. (4.3, 4.7)

C. (2,3, 7.3)

D. (3.3, 3.7)

3.5+-2*.8/sqrt(64)=3.5+-.2=3.5-.2=3.3; 3.5+.2=3.7

Explanation

3.5+-2*.8/sqrt(64)=3.5+-.2=3.5-.2=3.3; 3.5+.2=3.7

48. Theoretically, the "sampling distribution of sample mean" is which of the following?

The distribution of values of x in the population of interest.

The distribution of values of sample mean, but only in a very large samples.

The distribution of values of x in a specified sample from the population.

The distribution of values of sample mean from all possible samples of a specified size.

The histogram of values of x in a random sample of size n.

The "sampling distribution of sample mean" is the distribution of values of sample mean from all possible samples of a specified size.

Explanation

The "sampling distribution of sample mean" is the distribution of values of sample mean from all possible samples of a specified size.

49. The data in the table below represent distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at month. The line in the scatterplot is the least squares line:

where

y-hat is the predicted length of time and x=distance of shipment, in miles.

Why is the line on the scatter plot the least squares line?

The distances of the points to the line are as small as possible.

The sum of the squared residuals is as small as possible.

The predicted shipping time are identical to the actual shipping time used to determine the line.

The sum of the deviations of the shipping days from the mean shipping days is minimized

The predicted shipping days is as small as possible.

the least squares line is The sum of the squared residuals is as small as possible.

Explanation

the least squares line is The sum of the squared residuals is as small as possible.

50. The price of a pound of grapes in the grocery stores along the Wasatch Front is distributed normally with a mean of $1.40 and a standard deviation of $0.15. What is the probability that the mean price of a pound of grapes of four randomly selected grocery stores will exceed $1.60?

0.0038

0.0918

0.9962

0.9082

z=(1.6-1.4)/(0.15/sqrt(4))=2.67
Percentage to the right of z: 1-0.9962=0.0038

Explanation

z=(1.6-1.4)/(0.15/sqrt(4))=2.67
Percentage to the right of z: 1-0.9962=0.0038

51. Of the following statements about standard deviation, three statements True and one is False. Which statement is FALSE?

Standard deviation has a unit of measure.

Standard deviation is only positive.

Standard deviation is inflated by outliers.

Standard deviation should be used to measure spread even when the mean is not an appropriate measure of center.

Properties of Standard deviation:
1. Has a unit of measure
2. Can only be positive values.
3. Is affected by outliers. Outliers increases standard deviation.
4. It is appropriate measure of spread if the data is symmetric. When the data is symmetric, the mean is the appropriate measure of center.

Explanation

Properties of Standard deviation:
1. Has a unit of measure
2. Can only be positive values.
3. Is affected by outliers. Outliers increases standard deviation.
4. It is appropriate measure of spread if the data is symmetric. When the data is symmetric, the mean is the appropriate measure of center.

52. The mean amount of money spent by BYU single students on dates this semester was $380, with a standard deviation of $100. The distribution was skewed to the right. Suppose you took 20,000 simple random samples of 49 students, and computed the mean amount for each sample. Between what two values would you expect approximately 95% of the mean amounts for the samples to be?

$80 to $680

$351.4 to 408.6

$280 to $480

$100 to $380

stdev for x-bar=100/sqrt(49)=14.29
95% covers 2 stdev above and below the mean, therefore, 380-3(14.29)=351.4, and 380+3(14.29)=408.6

Explanation

stdev for x-bar=100/sqrt(49)=14.29
95% covers 2 stdev above and below the mean, therefore, 380-3(14.29)=351.4, and 380+3(14.29)=408.6

53. The data in the table below represent distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at month. The line in the scatterplot is the least squares line:

where

y-hat is the predicted length of time and x=distance of shipment, in miles.

For these data r² = 83.7%. Interpret r²in context.

Eighty-three point seven percent of delivery time is based on distance.

Distance explains 83.7% of the variation in delivery time.

Distance can be used to predict delivery time about 83.7% of the time.

Delivery time can be used to predict distance about 83.7% of the time.

r^2 is the percent variation in y that can be explained by x.

Explanation

r^2 is the percent variation in y that can be explained by x.

54. A survey conducted by the BYU-Salt Lake Center to assess the reasons students from BYU-Provo take classes at the Salt Lake Center instead of in Provo and obtained data from a sample of 1500 BYU-Provo students. The administration believes that BYU-Provo students take an average of 6 credits per semester at the BYU-SLC. The average number of credits taken by BYU-Provo students was found to be 11 with a standard deviation of 3. Is 6 a parameter or a statistic? Why?

A parameter because the average is for all students.

A parameter because it is the average for all students at BYU-Provo.

A statistic because it summarizes the results of the entire population of students at BYU-Provo.

A statistic because it summarizes the results of this sample of 1500 BYU-Provo students.

Parameter refers to population mean or population standard deviation or population proportion.
Statistics refers to sample mean or sample standard deviation or sample proportion.

Explanation

Parameter refers to population mean or population standard deviation or population proportion.
Statistics refers to sample mean or sample standard deviation or sample proportion.

55. The price of a pound of grapes in the grocery stores along the Wasatch Front is distributed normally with a mean of $1.40 and a standard deviation of $0.15. A store selling a pound of grapes for $1.60 is considered expensive. What is the probability that a randomly selected store is selling expensive grapes?

0.9082

0.9099

0.0918

0.0901

0.1600

z=(1.60-1.4)/0.15=1.33
From the Normal Table:
z Percentage to the left of z
1.33 .9082
The percentage to the right of z: 1-.9082=0.0918

Explanation

z=(1.60-1.4)/0.15=1.33
From the Normal Table:
z Percentage to the left of z
1.33 .9082
The percentage to the right of z: 1-.9082=0.0918

56. Which one of the following is a FALSE statement about the correlation coefficient r?

R is affected by outliers.

Values of r range from -1 to +1.

The correlation r has no unit of measure.

If the sign of r is negative, then increases in one variable are associated with decreases in the other variable.

The designations of which is the explanatory variable and which is the response variable cannot be interchanged.

We get the same correlation even if we interchange the explanatory and the response variables.

Explanation

We get the same correlation even if we interchange the explanatory and the response variables.

57. Imagine that we have a population that is skewed to the right. This population has a mean of 70 and a standard deviation of 10. Using a simulation program, Jesse simulated drawing all possible samples of size 8 from the population. He then plotted the means for each of the samples that he drew. Preston simulated drawing all possible samples of size 50, and he also plotted the means for each of the samples that he drew.

How would the mean of Jesse's distribution of sample means compare with the mean of Preston's distribution of sample means?

Preston's distribution would have a mean close to 70 but we cannot predict what the mean of Jesse's distribution would be.

Preston's distribution would have a mean closer to 70 than Jesse's distribution.

Jesse's distribution would have a mean closer to 70 than Preston's distribution.

They would both have the same mean of 70.

The mean of the sample means=the population mean, regardless of size.

Explanation

The mean of the sample means=the population mean, regardless of size.

58. Students who have taken Stats221 were asked in a survey about their Stats221 Final exam scores and how much time they spent studying for the class.The correlation coefficient between these two variables is 0.90. On the basis of this information, approximately what percentage of the variation in Stats221 Final exam score can be explained by how time students spent studying for the class?

90%

9%

81%

None of the above

(.90)^2=.81 or 81%

Explanation

(.90)^2=.81 or 81%

59. Consider a population that is non-Normally distributed with mean 70 and a standard deviation of 10. A sample size of 25 is taken from this population. Which of the following statements about the sampling distribution of sample means is true?

The sampling distribution of sample means is Normally distributed with standard deviation less than 10.

The sampling distribution of sample means is Normally distributed with standard deviation of 10.

The sampling distribution of sample means is Normally distributed with standard deviation greater than 10.

The sampling distribution of sample means is not Normally distributed with standard deviation less than 10.

The sampling distribution of sample means is not Normally distributed with standard deviation of 10.

When sampling from a non-Normal population, a large (n>=30) simple random sample must be taken for the Central Limit to hold that the shape of the sampling distribution is Normal.

Explanation

When sampling from a non-Normal population, a large (n>=30) simple random sample must be taken for the Central Limit to hold that the shape of the sampling distribution is Normal.

60. Imagine that we have a population that is skewed to the right. This population has a mean of 70 and a standard deviation of 10. Using a simulation program, Jesse simulated drawing all possible samples of size 8 from the population. He then plotted the means for each of the samples that he drew. Preston simulated drawing all possible samples of size 50, and he also plotted the means for each of the samples that he drew.

How would the standard deviation of Jesse's distribution of sample means compare to the standard deviation of Preston's distribution of sample means?

Preston's distribution would have a standard deviation close to 10 but we cannot predict what the standard deviation of Jesse's distribution would be.

Preston's distribution would have a standard deviation closer to 10 than Jesse's distribution.

Jesse's distribution would have a standard deviation closer to 10 than Preston's distribution.

Both distributions would have a standard deviation of 10.

Jesse's stdev of x-bars=10/sqrt(8)=3.5
Preston's stdev of x-bars=10/sqrt(50)=1.4

Explanation

Jesse's stdev of x-bars=10/sqrt(8)=3.5
Preston's stdev of x-bars=10/sqrt(50)=1.4

61. Select the appropriate symbol below for the mean of the sampling distribution of sample means.

A

B

C

D

E

The symbol B represents the mean of the sampling distribution of sample means. In statistics, the sampling distribution of sample means is the distribution of the means of all possible samples of a given size taken from a population. The mean of this sampling distribution is equal to the population mean. Therefore, symbol B is the appropriate choice for representing the mean of the sampling distribution of sample means.

Explanation

The symbol B represents the mean of the sampling distribution of sample means. In statistics, the sampling distribution of sample means is the distribution of the means of all possible samples of a given size taken from a population. The mean of this sampling distribution is equal to the population mean. Therefore, symbol B is the appropriate choice for representing the mean of the sampling distribution of sample means.