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Equations-Z = (X â�� M) / SDSD2 = SS / NSS = Î£(X-M)2M = Î£(X)/N
For the Z-Scores, please use the back of your book.
Questions and Answers
1.
What is the most representative measure of central tendency?
A.
The median, because it is the middle number
B.
The median, because it is the average of the numbers
C.
The mode, because it is the most recurring number
D.
The mean, because it is the average of the numbers
E.
The mean, because it is the middle number
Correct Answer D. The mean, because it is the average of the numbers
Explanation The mean is the most representative and is used most often. Only in skewed data would the median be referred to as the more accurate representation.
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2.
In which set of scores should you use the median instead of the mean?
Explanation When the data is skewed by a large outlier or extreme score (1), then the mean is biased and is no longer a good represenation for all of the scores. The median is now the better representation.
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3.
Which is the best measure of variability for a group of scores?
A.
The mean, because it is the average of the scores
B.
Average deviation, because it shows (on average) how the scores are spread out from the mean
C.
Variance, because it is describes the spread of the deviation scores
D.
Standard deviation, because it is labeled in usable units
E.
Variance, because it is the square root of standard deviation
Correct Answer D. Standard deviation, because it is labeled in usable units
Explanation Variance is the Standard Devation squared. By using Standard deviation, we are able to measure how spread out the scores are in "non-squared" units. For instance, saying "the scores are spread out on average about 2 units away from their mean" makes more sense than "the scores are spread out on average about 4 units squared away from their mean"
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4.
What is the symbol for the variance of the population?
A.
σ
B.
σ2
C.
SD
D.
SD2
E.
S
Correct Answer B. σ2
Explanation The symbol σ2 represents the variance of the population. Variance is a statistical measure that quantifies the spread or dispersion of a set of data points. It is calculated by taking the average of the squared differences between each data point and the mean of the population. The symbol σ represents the standard deviation of the population, which is the square root of the variance. Therefore, σ2 is the correct symbol for the variance of the population.
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5.
Suppose a recent study described a particular sample of 50 college students who watched MTV nonstop for 30 days straight. After administering a test of logic and reasoning, they were found to have a mean score of 70 with a variance of 25. What score would a person need to have to be in the top 5%?
A.
78.2
B.
70.2
C.
75
D.
111
E.
66.5
Correct Answer A. 78.2
Explanation 1.64 is the corresponding Z score to be ing the top 5%. SD= Square root of 25 = 5. Following the equation Z=(X-M)/SD, 1.64= (X - 70)/5 = 78.2
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6.
Referring to the previous question, if a person scored a 54 on the test, what would be their Z score?
A.
3.2
B.
-.64
C.
-4
D.
-3.2
E.
4
Correct Answer D. -3.2
Explanation Following the equation Z=(X-M)/SD, Z= (54 - 70)/5 = -4
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7.
There are 115 total people working on a computer in a library. 30 are studying for a history exam, 24 are completing statistics homework, and 61 are checking Facebook. Since all of the computers are taken, that means you will have to ask someone to leave. What is the probability that the person you ask will be checking Facebook or completing statistics homework?
A.
.17
B.
.85
C.
.53
D.
.21
E.
.74
Correct Answer E. .74
Explanation According to the equation Probability= Successful outcomes/All Possible outcomes, p= (61 + 24) / 115
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8.
John took a statistics aptitude test received a score of 12. Kayla took a different statistics test in and received 86. However, John made the case that even though Kayla received the higher score, his test was much more difficult and he actually has greater knowledge of statistics than her. How can John show Kayla that he actually has superior statistics knowledge?
(Assume both tests are normally distributed)Statistics for John’s Test: M= 8, SD=2
Statistics for Kayla’s Test: M= 60, SD=20
A.
John's score falls closer to Kayla's mean than does Kayla's score to John's mean
B.
John's score falls closer to his mean than does Kayla's score to her mean
C.
John's mean/SD proportion is larger than Kayla's mean/SD proportion
D.
Kayla's score falls closer to her mean than does John's score to his mean
E.
None of the above
Correct Answer D. Kayla's score falls closer to her mean than does John's score to his mean
Explanation John's score of 12 falls 2 standard deviations above its mean, while Kayla's score of 86 only falls 1.3 standard deviations about its mean. John has the more extreme score because he falls further away from the mean, which means he actually received the higher score.
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9.
The following is data regarding hours studied in a statistics class:41751036289What is the SD for this set of scores?
A.
2.88
B.
8.25
C.
82.5
D.
0
E.
5.5
Correct Answer A. 2.88
Explanation According to the equation Variance=SS/N, SS=82.5, Variance= 8.25, SD=2.88
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10.
A variable is different from a value in that:
A.
A variable is a possible number or category that a value can have
B.
A value is a particular person's score, whereas a variable is the characteristic being measured
C.
The variable is the characteristic being measured, and a value is a possible number or category a score can have
D.
A variable is a categorical variable, but a value is a numeric variable
E.
A variable can vary, but a value has no range
Correct Answer C. The variable is the characteristic being measured, and a value is a possible number or category a score can have
Explanation A variable is the characteristic being measured in a study or experiment, while a value is a possible number or category that a score can have within that variable. In other words, the variable represents the concept or attribute being studied, while the value represents the specific measurement or category within that concept. For example, in a study on height, "height" is the variable being measured, and values could be "5 feet 10 inches" or "6 feet 2 inches".
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11.
How many clubs you are apart of at Maryville is an example of:
A.
A categorical variable
B.
A nominal variable
C.
An equal-interval variable
D.
An ordinal variable
E.
An equal-interval ratio variable
Correct Answer E. An equal-interval ratio variable
Explanation Equal interval ratio variables are numeric variables that can have an absolute zero (you can be apart of 0 clubs)
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12.
What would this distribution be called?
A.
Kurtotic Skew
B.
Right/Postive Skew
C.
Ceiling Effect
D.
Left/Postive Skew
E.
Right/NegativeSkew
Correct Answer B. Right/Postive Skew
Explanation Since the tail is being pulled in the positive (right) direction, this is a right skewed [aka positive skewed] distribution
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13.
Drawing conclusions that go beyond the number from a research study is/are:
A.
Descriptive Statistics
B.
Variability
C.
The Z Distribution
D.
Inferential Statistics
E.
Probability
Correct Answer D. Inferential Statistics
Explanation Inferential statistics involves drawing conclusions or making inferences about a population based on a sample. It allows researchers to generalize their findings and make predictions about the larger population. This is in contrast to descriptive statistics, which simply summarize and describe the data without making any inferences. Variability refers to the spread or dispersion of data, the Z distribution is a specific type of probability distribution used in hypothesis testing, and probability is the likelihood of an event occurring.
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14.
In a study, “All College Students” are the ______________ while “Maryville Students” are the ______________.
A.
Sample, Population
B.
Group, Sample
C.
Subjects, Population
D.
Sample, Subjects
E.
Population, Sample
Correct Answer E. Population, Sample
Explanation "All College Students" is the large population from which the sample ("Maryville Students") are drawn.
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15.
If you were doing a study on Maryville Students and you chose people from your Statistics class to be the subjects, what kind of selection would this be?
A.
Random
B.
Exclusive
C.
Selective Convenience
D.
Haphazard
E.
Problematic
Correct Answer D. Haphazard
Explanation This selection would be considered haphazard because the subjects are chosen without any specific criteria or randomization. It is a careless and unplanned selection process, which may introduce bias and affect the validity and generalizability of the study's findings.
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16.
How many times something is supposed to happen over the long run is called:
A.
Relative Frequency
B.
Expected Frequency
C.
Expected Relative Frequency
D.
Frequency
E.
Probability
Correct Answer C. Expected Relative Frequency
Explanation Expected Relative Frequency refers to the number of times an event is expected to occur in the long run, based on probability. It takes into account the likelihood of the event happening and provides an estimate of the frequency of occurrence over a large number of trials. This concept is commonly used in statistics and probability theory to make predictions and analyze data.
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