Deck 7: Testing One Sample Mean

Question 1

Although their formulas are similar, one difference between a z-score (z) and a t-statistic (t) is that a z-score evaluates ______ but a t-statistic evaluates ______.

A) sample means; individual scores for a variable
B) individual scores for a variable; sample means
C) scores; probabilities
D) normal distributions; skewed distributions

Answer 1

individual scores for a variable; sample means

Question 2

I draw a random sample from the population and calculate the mean of this sample . If I were to do this an infinite number of times, I could create ______.

A) the sampling distribution of the mean
B) the null hypothesis
C) the standard normal distribution (normal curve)
D) the standard deviation

Answer 2

the sampling distribution of the mean

Question 3

The ______ is the distribution of values of the sample mean for an infinite number of samples of size N that are randomly selected from the population.

A) sampling distribution
B) standard error of the mean
C) sampling distribution of the mean
D) population standard error of the mean

Answer 3

sampling distribution of the mean

Question 4

Although their formulas are similar, one difference between the z-score (z) and the t-statistic (t) is that ______.

A) only the denominator of the z-score formula (not the t-statistic) is a measure of variability
B) z-scores evaluate sample means whereas t-statistics evaluate individual scores
C) only the numerator of the z-score formula (not the t-statistic) is the difference between means
D) the z-score evaluates individual scores whereas the t-statistic evaluates sample means

Question 5

Although their formulas are similar, one primary difference between a z-score (z) and a t-statistic (t) is that the ______ of the formula for the t-statistic involves ______.

A) denominator; the variability of individual scores (Xs), not the variability of sample means
B) numerator; difference between a score (X) and a population mean (μ)
C) denominator; the variability of sample means , not the variability of individual scores (Xs)
D) numerator; the difference between a score (X) and a sample mean

Question 6

A researcher draws a random sample of 25 people from a population and calculates the mean of their IQs. If she were to repeat this process of drawing samples and calculating means an infinite number of times, the sample means could be used to create ______.

A) the sampling distribution of the mean
B) critical values
C) z-scores
D) research hypotheses

Question 7

The ______ of the sampling distribution of the mean may be represented by ______.

A) symmetry; 0
B) variability; 1
C) modality; s
D) variability;

Question 8

Although their formulas are similar, one difference between the z-score (z) and the t-statistic (t) is that ______.

A) only z-scores (not t-statistics) are part of a theoretical distribution
B) z-scores evaluate sample means whereas t-statistics evaluate individual scores
C) the numerator of the t-statistic formula (not the z-score) is the difference between a score and a mean
D) the denominator of the t-statistic formula estimates the variability of sample means rather than individual scores

Question 9

The ______ of the sampling distribution of the mean is represented by ______.

A) mean; µ
B) variability; s
C) mean; 1
D) variability;

Question 10

The sampling distribution of the mean helps ______.

A) determine the probability of obtaining a particular value of the population mean (µ)
B) describe the modality of a set of data
C) determine whether a set of data is skewed (asymmetric)
D) determine the probability of obtaining a particular value of a sample mean

Question 11

The variability of the sampling distribution of the mean may be represented by ______.

A) 0
B)
C) σ
D) s

Question 12

The ______ of the sampling distribution of the mean may be represented by ______.

A) mean; 0
B) variability;
C) mean;
D) variability; 0

Question 13

Which of the following is a similarity of the t-distribution and the standard normal distribution?

A) There is only one distribution for each.
B) Both distributions are symmetrical.
C) Both distributions are asymmetrical.
D) Both distributions are a function of the sample size.

Question 14

The sampling distribution of the mean helps us ______.

A) calculate descriptive statistics
B) set alpha (α)
C) determine the probability of a sample mean
D) determine whether our variables are normally distributed

Question 15

The sampling distribution of the mean ______.

A) is used to set alpha (α)
B) helps researchers evaluate sample means
C) is based on an infinite number of z-scores
D) is also known as the 'normal curve'

Question 16

Although their formulas are similar, one primary difference between a z-score (z) and a t-statistic (t) is that the ______ of the formula for the t-statistic contains or involves ______.

A) denominator; a sample mean rather than the population mean (μ)
B) numerator; a sample mean rather than an individual score (X)
C) numerator; the variability of individual scores (Xs) rather than sample means
D) denominator; the population mean (μ) rather than a sample mean

Question 17

Holding all else constant, as sample size increases, the sampling distribution of the mean ______.

A) becomes flatter
B) has greater variability
C) becomes skewed
D) becomes more peaked

Question 18

A ______ is used to evaluate ______.

A) z-score; the mean of a sample
B) t-test; the difference between two means
C) z-score; the difference between a sample mean and a population mean
D) t-test; a score on a variable

Question 19

The mean of the sampling distribution of the mean is equal to ______.

A)
B) 1
C) 0
D) µ

Question 20

The ______ of the sampling distribution of the mean is equal to ______.

A) mean; 0
B) variability; 0
C) variability; 1
D) mean; µ

Question 21

The central limit theorem states that when an infinite number of random samples are drawn from a population, the sample means are approximately normally distributed with a mean equal to the ______ and a standard deviation equal to the ______ of the mean.

A) population mean; standard error
B) population mean; standard deviation
C) sample mean; standard error
D) sample mean standard deviation

Question 22

The statement "µ ≠ 3" would be part of a ______.

A) non-directional alternative hypothesis
B) directional alternative hypothesis
C) non-directional null hypothesis
D) directional null hypothesis

Question 23

A ______ symbol in the ______ hypothesis implies this hypothesis is ______.

A) >; null; one-tailed
B) ≠; null; directional
C) ≠; alternative; non-directional
D) =; alternative; one-tailed

Question 24

A '≠' symbol in the ______ hypothesis implies this hypothesis is ______.

A) null; directional
B) null; two-tailed
C) alternative; one-tailed
D) alternative; non-directional

Question 25

The statement µ > 3 is an example of a ______.

A) directional (one-tailed) null hypothesis
B) directional (one-tailed) alternative hypothesis
C) non-directional (two-tailed) null hypothesis
D) non-directional (two-tailed) alternative hypothesis

Question 26

The statement µ < 10 is an example of a ______.

A) directional (one-tailed) alternative hypothesis
B) directional (one-tailed) null hypothesis
C) non-directional (two-tailed) alternative hypothesis
D) non-directional (two-tailed) null hypothesis

Question 27

The statement µ > 3 is an example of a ______.

A) directional null hypothesis
B) directional alternative hypothesis
C) non-directional null hypothesis
D) non-directional alternative hypothesis

Question 28

What is the sufficient sample size to use for the central limit theorem?

A) at least 25
B) at least 26
C) at least 30
D) at least 31

Question 29

The modality, symmetry, and variability of the sampling distribution of the mean are defined by a statistical principle known as ______.

A) random sampling
B) ratio scale of measurement
C) standard error of the mean
D) central limit theorem

Question 30

The statement "µ ≠ 3" would be part of a ______.

A) two-tailed, directional hypothesis
B) two-tailed, non-directional hypothesis
C) one-tailed, directional hypothesis
D) one-tailed, non-directional hypothesis

Question 31

Standard deviation measures the ______ for a variable, standard error represents the ______ calculated from samples.

A) variability of statistics; variability of scores
B) variability of scores; variability of statistics
C) variability of scores; error of scores
D) variability of statistics; error of scores

Question 32

This distribution provides an illustration of a ______.

A) one-tailed null hypothesis
B) directional null hypothesis
C) directional alternative hypothesis
D) two-tailed alternative hypothesis

Question 33

Which of the following is a correctly stated alternative hypothesis?

A) H₁: µ ≠ 3
B) H₁: µ = 3
C) H₁: = 3
D) H₁: > 3

Question 34

A ______ alternative hypothesis (one that may have an ______ symbol) is also referred to as ______.

A) directional; ≠ ; one-tailed
B) non-directional; <; two-tailed
C) non-directional; >; asymmetrical
D) non-directional; ≠; two-tailed

Question 35

A ______ symbol in the ______ hypothesis implies this hypothesis is ______.

A) <; alternative; one-tailed
B) ≠; null; two-tailed
C) >; null; non-directional
D) ≠; alternative; directional

Question 36

A ______ alternative hypothesis such as ______ is also referred to as ______.

A) directional; µ ≠ 164; two-tailed
B) non-directional; µ > 164; two-tailed
C) directional; µ > 164; one-tailed
D) non-directional; µ ≠ 164; one-tailed

Question 37

A ______ alternative hypothesis (one that may have a ______ symbol) is also referred to as ______.

A) directional; ≠ ; two-tailed
B) non-directional; =; two-tailed
C) directional; >; one-tailed
D) non-directional; ≠; one-tailed

Question 38

Which of the following is a correctly stated alternative hypothesis?

A) H₁: ≠ 3
B) H₁: µ = 3
C) H₁: α = .05 (two-tailed)
D) H₁: µ ≠ 3

Question 39

Which of the following is a correctly stated null hypothesis?

A) H₀: µ ≠ 3
B) H₀: = 3
C) H₀: µ = 3
D) H₀: = 3

Question 40

The '>' symbol would appear in the ______ hypothesis and would imply that this hypothesis is ______.

A) null; non-directional
B) null; two-tailed
C) alternative; one-tailed
D) alternative; non-directional

Question 41

Imagine that for a population of 200, the mean is 20.23 with a standard deviation of 5.12. What is the population standard error of the mean ?

A) .003
B) .03
C) .36
D) .50

Question 42

This distribution illustrates a ______.

A) non-directional null hypothesis
B) directional null hypothesis
C) non-directional alternative hypothesis
D) directional alternative hypothesis

Question 43

Imagine that for a population of 40, the mean is 10.25 with a standard deviation of 2.10. What is the population standard error of the mean ?

A) .03
B) .33
C) .34
D) .36

Question 44

For a z-statistic of -1.34, one would conclude (for a two-tailed test) the score is ______.

A) significant at the .05 level but not the .01 level
B) significant at both the .05 level and the .01 level
C) not significant
D) not significant at the .05 level but is significant at the .01 level

Question 45

Using the following information, calculate the z-statistic for the z-test for one mean. = 27 μ = 15 = 1.50

A) -8.00
B) 8.00
C) 4.00
D) -.10

Question 46

For a z-statistic of 2.79, one would conclude (for a two-tailed test) the score is ______.

A) significant at the .05 level but not the .01 level
B) significant at both the .05 level and the .01 level
C) not significant
D) not significant at the .05 level but is significant at the .01 level

Question 47

Using the following information, calculate the z-statistic for the z-test for one mean. = 31.75 μ = 25.67 = 2.45

A) 2.48
B) -2.48
C) .10
D) -.10

Question 48

Using the following information, calculate the z-statistic for the z-test for one mean. = 15 μ = 22 = 3.50

A) 2.00
B) -2.00
C) 1.23
D) -3.13

Question 49

For a z-statistic of -1.34, the decision about the null hypothesis is ______.

A) do not reject the null hypothesis (p > .05)
B) do not reject the null hypothesis (p < .01)
C) reject the null hypothesis (p > .05)
D) reject the null hypothesis (p < .05)

Question 50

A population has a mean of 15.21 and a standard deviation of 1.56. For a sample of N = 20, what is the population standard error of the mean ?

A) .35
B) .36
C) 1.56
D) 4.47

Question 51

A population has a mean of 55.25 and a standard deviation of 14.23. For a sample of N = 100, what is the population standard error of the mean ?

A) 7.03
B) 3.77
C) 1.43
D) 1.42

Question 52

Using the following information, calculate the z-statistic for the z-test for one mean. = 154 μ = 145 = 15.25

A) 9.00
B) -9.00
C) .59
D) -.59

Question 53

A population has a mean of 606 and a standard deviation of 23. For a sample of N = 500, what is the population standard error of the mean ?

A) .10
B) 1.02
C) 1.03
D) 1.1

Question 54

For a z-statistic of 1.89, one would conclude (for a two-tailed test) the score is ______.

A) significant only at the .05 level
B) significant at both the .05 level and the .01 level
C) not significant
D) not significant at the .05 level but is significant at the .01 level

Question 55

Using the following information, calculate the z-statistic for the z-test for one mean. = 101 μ = 109 = 3.44

A) -2.32
B) 2.32
C) -2.33
D) 2.33

Question 56

If the calculated value of a z-statistic ______ the critical value, you would say ______.

A) does not exceed; p < .01
B) does not exceed; p < .05
C) does not exceed; p > .05
D) exceeds; p > .05

Question 57

The decision to use a directional versus non-directional alternative hypothesis most directly affects ______.

A) the critical value(s)
B) alpha ()
C) the sample size
D) the degrees of freedom

Question 58

A researcher has calculated a z-statistic of 1.92. For a two-tailed test with alpha () = .05, which of the following is the most appropriate?

A) do not reject the null (p < .05)
B) do not reject the null (p > .05)
C) reject the null (p < .05)
D) reject the null (p > .05)

Question 59

For a z-statistic of 2.22, one would conclude (for a two-tailed test) the score is ______.

A) significant at the .05 level but not the .01 level
B) significant at both the .05 level and the .01 level
C) not significant
D) not significant at the .05 level but is significant at the .01 level

Question 60

If the value of a calculated z-statistic ______ the critical value, you would say ______.

A) exceeds; p > .05
B) exceeds; p < .05
C) does not exceed; p < .05
D) does not exceed; p < .01

Question 61

If I wanted to measure the variability of ______ , I would calculate ______.

A) individual scores (Xs); the standard error of the mean
B) sample means ; the standard error of the mean

C) sample means ; the standard deviation (s)
D) individual scores (Xs); the sample mean

Question 62

In testing the mean of a sample, calculating a positive value of the t-statistic (t) necessarily implies ______.

A) the research hypothesis has been supported
B) you have done your calculations correctly (without making a mistake)
C) the value of the t-statistic falls in the region of rejection
D) the sample mean is greater than the hypothesized population mean

Question 63

In testing the mean of a sample, calculating a negative value of the t-statistic (t) indicates ______.

A) the sample mean is less than the hypothesized population mean
B) the score is less than the mean
C) is greater than
D) you have made an error in your calculations

Question 64

In testing the mean of a sample, the sample mean is transformed into a t-statistic in order to ______.

A) determine the critical values
B) prove our research hypotheses
C) determine whether the alternative hypothesis (H₁) should be one-tailed or two-tailed
D) determine the probability of obtaining the value of the sample mean

Question 65

Holding all else constant, as sample size increases, the value of the standard error of the mean ______.

A) increases
B) decreases
C) stays the same
D) explodes

Question 66

You collect data from a sample of 150 people, and calculate a mean of 6.87 and a standard deviation of 3.69. What is the value for the standard error of the mean ?

A) .30
B) 1.86
C) 6.87
D) 21.83

Question 67

Which of the following can be a negative number in testing the mean of a sample?

A) the degrees of freedom
B) the critical values
C) alpha
D) the standard error of the mean

Question 68

Looking at the degrees of freedom tells you something about ______.

A) the size of the sample
B) the directionality of the alternative hypothesis
C) the level of significance of a statistic
D) the research hypothesis

Question 69

Which of the following can be a negative number in testing the mean of a sample?

A) t
B) df
C)
D) α

Question 70

Looking at ______ for a statistic like a t-statistic provides an indication of the directionality of the alternative hypothesis.

A) the null hypothesis
B) alpha
C) the critical values
D) the sample size

Question 71

Which of the following would be the most accurate way to report the following z-test?

A) z = 2.55 < 2.58 ; p < .01
B) z = 2.55 < 2.58 ; p > .05
C) z = 2.55 < 2.58 ; p < .05
D) z = 2.55 < 2.58 ; p > .01

Question 72

Looking at the ______ for a statistic like a t-statistic provides an indication of the sample size in a study.

A) research hypothesis
B) null hypothesis
C) degrees of freedom
D) alternative hypothesis

Question 73

Looking at the degrees of freedom for a statistic like a t-statistic provides information regarding ______.

A) the size of the sample
B) the sample mean
C) whether alpha is one-tailed or two-tailed
D) the population mean (μ)

Question 74

You collect data from a sample of 150 people and calculate a mean of 6.87 and a standard deviation of 3.69. What is the value for the standard error of the mean ?

A) .16
B) .30
C) 3.69
D) 12.24

Question 75

In testing the mean of a sample, the sample mean is transformed into a ______ statistic in order to ______.

A) z; decide whether to set alpha at .05 or .01
B) t; determine the probability of a sample mean
C) z; determine the critical values
D) t; determine whether the distribution of sample means is normal

Question 76

A ______ can represent the variability of ______.

A) standard deviation; sample means
B) standard deviation; differences between two sample means
C) standard error; individual scores (X)
D) standard error; sample means

Question 77

Reporting the results of a z-test results typically includes all of the following EXCEPT ______.

A) the variable analyzed
B) the standard error of the sample mean
C) the sample and population means
D) the level of significance

Question 78

From data collected from a sample of 100 people, you obtain a mean of 16.27 and a standard deviation of 4.56. What is the value for the standard error of the mean ?

A) .46
B) .05
C) .16
D) 4.56

Question 79

If I wanted to estimate the variability of sample means , I would calculate ______.

A) the standard error of the mean
B) the standard deviation (s)
C) z-scores
D) the population mean (μ)

Question 80

If I wanted to measure the variability in a set of scores (Xs), I would calculate ______.

A) the standard error of the mean
B) the standard deviation (s)
C) z-scores
D) the t-statistic