Deck 10: The Paired-Samples T Test

Question 1

A clinical researcher was interested in determining whether her interventions were effective in minimizing depression symptoms among participants.To assess the effectiveness of the treatment program, she administered a depression inventory prior to treatment and after treatment.She hypothesized that depression scores would be lower at time two compared to time one.She then compared the mean differences between the two groups and found that the treatment was effective.The researcher's hypothesis is:

A) one-tailed.
B) two-tailed.
C) not supported.
D) supported by null hypothesis.

Answer 1

one-tailed.

Question 2

In a within-groups design with two groups, the appropriate hypothesis test is a(n):

A) single-sample t test.
B) two-way analysis of variance.
C) paired-samples t test.
D) independent-samples t test.

Answer 2

paired-samples t test.

Question 3

One of the first steps in calculating the dependent-samples t statistic is:

A) counterbalancing the order of the calculations.
B) finding the variance for each of the measured variables and then pooling them.
C) creating a difference score for each participant in the sample.
D) averaging the scores on each of the measured variables and finding the difference between those means.

Answer 3

creating a difference score for each participant in the sample.

Question 4

A clinical researcher was interested in determining whether her interventions were effective in minimizing depression symptoms among participants.To assess the effectiveness of the treatment program, she administered a depression inventory prior to treatment and after treatment.She hypothesized that depression scores would be lower at time two compared to time one.She then compared the mean differences between the two groups and found that the treatment was effective.The independent variable in this study is:

A) depression scores.
B) gender.
C) age.
D) time.

Question 5

Another name for a paired-samples t test is the _____ t test.

A) single-sample
B) dependent-samples
C) independent-samples
D) no-sample

Question 6

The formula for the research hypothesis for a paired-samples t test is:

A) H₀: $\mu$ ₁ = $\mu$ _2.
B) H₀: $\mu$ ₁ $\neq$ $\mu$ _2.
C) H₁: $\mu$ ₁ = $\mu$ _2.
D) H₁: $\mu$ ₁ $\neq$ $\mu$ _2.

Question 7

Twenty college students experience the effects of alcohol on reaction time.They perform very basic timed responses in a driving simulator both before and after consuming several alcoholic beverages.The researcher collects a reaction-time result for each of the 20 students before and after intoxication, for a total of 40 measures.What is the null hypothesis for this paired-samples study?

A) There is no difference in reaction time before and after consuming alcohol.
B) Reaction time slows with alcohol consumption.
C) There is a difference in reaction time before and after consuming alcohol.
D) Reaction time quickens with alcohol consumption.

Question 8

The comparison distribution in a paired-samples t test is a distribution of:

A) mean difference scores.
B) differences between means.
C) means.
D) scores.

Question 9

According to the null hypothesis, the mean difference for the comparison distribution in a paired-samples t test is:

A) always 0.
B) sometimes 0.
C) always 1.
D) sometimes 1.

Question 10

When conducting a paired-samples t test, the sample mean difference is compared to:

A) a distribution of mean differences.
B) sample means.
C) differences between means.
D) the t distribution.

Question 11

The formula for the null hypothesis for a paired-samples t test is:

A) H₀: $\mu$ ₁ = $\mu$ _2.
B) H₀: $\mu$ ₁ $\neq$ $\mu$ _2.
C) H₁: $\mu$ ₁ = $\mu$ _2.
D) H₁: $\mu$ ₁ $\neq$ $\mu$ _2.

Question 12

A researcher studies 45 volunteer citizens from a small community and asks them about the amount of caffeine (in milligrams) they ingest before and after lunch each day.The null hypothesis for this paired-samples study could be:

A) more caffeine is ingested before lunch.
B) more caffeine is ingested after lunch.
C) there is a difference between the amount of caffeine ingested before and after lunch.
D) there is no difference between the amount of caffeine ingested before and after lunch.

Question 13

A study by Bettmann (2007) published in the Journal of the American Psychoanalytic Association assessed whether the attachment relationships between adolescents and their parents change as a result of a residential wilderness treatment experience for the adolescents.Participants completed the Adolescent Attachment Questionnaire at the start and at the end of the wilderness program.Which statistical test should be used to determine whether the wilderness treatment affected attachment relationships?

A) single-sample t test
B) z test
C) effect size test
D) paired-samples t test

Question 14

A clinical researcher was interested in determining whether her interventions were effective in minimizing depression symptoms among participants.To assess the effectiveness of the treatment program, she administered a depression inventory prior to treatment and after treatment.She hypothesized that depression scores would be lower at time two compared to time one.She then compared the mean differences between the two groups and found that the treatment was effective.The dependent variable in this study is:

A) depression scores.
B) gender.
C) age.
D) time.

Question 15

What is the mean of the difference scores for the following difference scores: 2, 6.5, 3, 7.8, 10, 4.2?

A) 7.10
B) 5.58
C) 6.7
D) 33.5

Question 16

In a paired-samples t test, the comparison distribution is a distribution of:

A) mean difference scores.
B) raw score differences.
C) median distribution scores.
D) means.

Question 17

Which of these is NOT an assumption of the paired-samples t test?

A) The dependent variable is a scale variable.
B) Participants are randomly selected.
C) There are fewer than 30 sample data.
D) The population is normally distributed.

Question 18

Twenty people participate in a weight-loss program for 2 months.Their weights after the 2 months are compared to their starting weights.What kind of mean difference might be expected if the null hypothesis is true for a paired-samples t test?

A) a loss of pounds, on average, showing the effectiveness of the program
B) a negative mean difference, indicating significant weight loss
C) no change in weight or weight gain, indicating that the program does not work
D) weight loss, indicating that the program does not work

Question 19

A psychologist is interested in whether working memory is influenced by sleep loss.The psychologist administers a measure of working memory to a group of subjects at 8 a.m..on Day 1 of the study and then again at 8 a.m.on Day 2 of the study, after keeping the subjects awake the entire night.Does sleep loss affect working memory? What statistical analysis should be performed to answer this question?

A) single-sample t test
B) z test
C) standard deviation analysis
D) paired-samples t test

Question 20

A researcher studies 45 volunteer citizens from a small community and asks them about the amount of caffeine (in milligrams) they ingest before and after lunch each day, a phenomenon assumed to be normally distributed.Which assumption for the paired-samples t test is NOT met in this research design?

A) The dependent variable is a scale variable.
B) Participants are randomly selected.
C) The population is normally distributed.
D) All the assumptions are met.

Question 21

The formula for the degrees of freedom for the paired-samples t test is:

A) N.
B) df_X + df_Y.
C) N - 1.
D) (N - 1)(N - 1).

Question 22

What would be the decision for the following paired-samples t test: t(24) = 1.11, p > 0.05?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 23

A paired-samples test is reported as t(18) = 1.73.What decision about this test should be made, assuming a two-tailed hypothesis test with a p level of 0.05?

A) fail to reject the research hypothesis
B) fail to reject the null hypothesis
C) reject the null hypothesis
D) reject the research hypothesis

Question 24

What would be the decision for the following paired-samples t test: t(24) = 4.11, p < 0.05?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 25

Twenty college students experience the effects of alcohol on reaction time.They perform very basic timed responses in a driving simulator both before and after consuming several alcoholic beverages.The researcher collects a reaction time result for each of the 20 students before and after intoxication, for a total of 40 measures.What are the degrees of freedom for this study?

A) 19
B) 20
C) 39
D) 40

Question 26

What is the paired-samples t test statistic for the following difference scores: -1, -24, +20, -28, -4?

A) -0.92
B) -0.85
C) 6.96
D) 8.67

Question 27

For the following data, what is the standard error of the difference scores? $$\begin{array} { | r r } \hline { \text { Before } } & \text { After } \\\hline 160 & 153 \\\hline 125 & 124 \\\hline 142 & 136 \\\hline 187 & 167 \\\hline\end{array}$$

A) 8.10
B) 4.26
C) 4.05
D) 2.10

Question 28

The critical cutoff(s) for a one-tailed, paired-samples t test with 16 participants at a p level of 0.05 is (are):

A) -1.746 or 1.746.
B) -1.753 or 1.753.
C) -2.120 and 2.120.
D) -2.132 and 2.132.

Question 29

The critical cutoff(s) for a two-tailed, paired-samples t test with 24 participants at a p level of 0.05 is (are):

A) -2.074 and 2.074.
B) -2.069 or 2.069.
C) -1.714 and 1.714.
D) -1.711 or 1.711.

Question 30

Assume the following for a paired-samples t test: N = 12, M_difference = 635.65, s = 608.50.What is the t statistic?

A) 183.50
B) 52.97
C) 3.62
D) 1.04

Question 31

For the following data, what is the mean of the difference scores? $$\begin{array} { | r r } \hline { \text { Before } } & \text { After } \\\hline 160 & 153 \\\hline 125 & 124 \\\hline 142 & 136 \\\hline 187 & 167 \\\hline\end{array}$$

A) 8.50
B) 5.00
C) 4.26
D) 11.33

Question 32

What is the paired-samples t test statistic for the following difference scores: 2, 6.5, 3, 7.8, 10, 4.2?

A) 7.10
B) 5.58
C) 4.46
D) 1.25

Question 33

Assume the following for a paired-samples t test: N = 9, M_difference = 13.19, s = 22.3.What is the t statistic?

A) 0.59
B) 1.77
C) 4.40
D) 7.43

Question 34

For the following data, what is the paired-samples t test statistic? $$\begin{array} { | r r } \hline \text { Before } & \text { After } \\\hline 160 & 153 \\\hline 125 & 124 \\\hline 142 & 136 \\\hline 187 & 167 \\\hline\end{array}$$

A) 8.10
B) 4.05
C) 2.10
D) 1.17

Question 35

The denominator (bottom portion) of the ratio for calculating the paired-samples t statistic is the:

A) pooled variance.
B) estimated standard error of the distribution of mean difference scores.
C) estimated standard error of the sampling distribution of the mean.
D) estimated standard deviation.

Question 36

What is the mean difference of the following difference scores: -1, -24, +20, -28, -4?

A) -6.40
B) -7.40
C) 6.17
D) 9.25

Question 37

What is the standard error of the difference scores for a paired-samples t test for the following difference scores: 2, 6.5, 3, 7.8, 10, 4.2?

A) 46.69
B) 3.06
C) 1.25
D) 0.03

Question 38

What is the formula for the paired-samples t test?

A) $\frac { \left( M - \mu _ { M } \right) } { s _ { M } }$
B) $\frac { \left( M _ { X } - M _ { Y } \right) } { s _ { \text {dfterence } } }$
C) $\frac { \left( M _ { \text {sffirenec } } - 0 \right) } { S _ { M } }$
D) $\frac { \left( M - \mu _ { M } \right) } { \sigma _ { M } }$

Question 39

What is the standard error for the paired-samples t test for the following difference scores: -1, -24, +20, -28, -4?

A) -0.92
B) -0.85
C) 6.96
D) 8.67

Question 40

The critical cutoffs for a two-tailed, paired-samples t test with seven participants at a p level of 0.01 are:

A) -2.447 and 2.447.
B) -2.998 and 2.998.
C) -3.143 and 3.143.
D) -3.708 and 3.708.

Question 41

What would be the decision for a two-tailed paired-samples t test where the confidence interval was determined to be [1.34, 6.45]?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 42

A paired-samples t test is reported as t(15) = 0.918, p > 0.05, d = 0.17.What is the effect size for this statistical test?

A) There is no effect size reported.
B) This is a small effect.
C) This is a medium effect.
D) This is a large effect.

Question 43

The formula for calculating effect sizes for the paired-samples t test replaces the _____ symbol used in the formula for the t statistic with the _____ symbol.

A) s; s_M
B) s_M; s
C) $\mu$ ; $\mu$ _M
D) $\mu$ _M; $\mu$

Question 44

Assume the following for a paired-samples t test: N = 19, M_difference = 13.19, s = 22.3.What is the 95 percent confidence interval for a two-tailed test?

A) [11.09, 15.29]
B) [8.07, 18.31]
C) [2.44, 23.94]
D) [-10.76, 10.76]

Question 45

What would be the decision for a two-tailed paired-samples t test where the confidence interval was determined to be [-3.45, -0.61]?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 46

The correct formula for effect size using Cohen's d for a paired-samples t test is:

A) (M - $\mu$ )/s + $\sigma$ .
B) (M - $\mu$ )/s.
C) (X - $\mu$ )/s.
D) ( $\sigma$ - $\mu$ )/s.

Question 47

What would be the decision for a two-tailed paired-samples t test where the confidence interval was determined to be [-3.45, 2.61]?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 48

What would be the decision for a two-tailed paired-samples t test where the t statistic is -4.67, with cutoffs of ±2.776?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 49

What is the 95 percent confidence interval for a two-tailed test for the following difference scores: -1, -24, +20, -28, -4?

A) [-12.92, 25.71]
B) [-16.67, 31.47]
C) [-25.72, 12.92]
D) [-31.47, 16.67]

Question 50

When conducting a paired-samples t test, one can assess the research hypothesis and get a range of mean differences that could be expected in the future using:

A) a hypothesis test.
B) an effect size measure.
C) post-hoc tests.
D) a confidence interval.

Question 51

What would be the decision for a two-tailed paired-samples t test where the t statistic is 4.67, with cutoffs of ±2.776?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 52

What would be the decision for a two-tailed paired-samples t test where the t statistic is -2.67, with cutoffs of ±2.776?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 53

A researcher investigates whether chocolate affects mood.She recruits college students to take a mood inventory, ingest a quarter pound of chocolate, and then complete the mood inventory again.Given the confidence interval [2.34, 5.41], what decision about the hypothesis should be made?

A) Reject the null hypothesis and conclude that chocolate affected mood because 0, or no effect, does not fall within the confidence interval.
B) Reject the null hypothesis and conclude chocolate lowers mood because the confidence interval includes small numbers.
C) Fail to reject the null hypothesis because the confidence interval is positive.
D) Fail to reject the null hypothesis and conclude the effect size is small for this study.

Question 54

Assume the following for a paired-samples t test: N = 9, M_difference = 101.4, s = 450.2.What is the 90 percent confidence interval for a two-tailed test?

A) [-177.72, 380.52]
B) [-101.4, 101.4]
C) [-48.67, 251.47]
D) [99.54, 103.26]

Question 55

The final step in calculating a confidence interval for a paired-samples t test is to convert the:

A) effect sizes to t scores.
B) t statistics into raw mean differences.
C) t statistics into z statistics.
D) z statistics into t statistics.

Question 56

Assume the following for a paired-samples t test: N = 19, M_difference = 13.19, s = 22.3.What is the effect size using Cohen's d?

A) 0.22
B) 0.41
C) 0.59
D) 2.58

Question 57

When conducting a paired-samples t test, one can assess the practical importance of the obtained results by calculating:

A) a hypothesis test.
B) an effect size measure.
C) post-hoc tests.
D) a confidence interval.

Question 58

A researcher investigates whether the extent to which people care about keeping their house clean and neat changes if they are given new things in that home.He follows eight families that were selected to receive home makeovers, assessing their cleanliness before the makeover and after.Given the confidence interval [-1.26, 0.95], what decision about the hypothesis should be made?

A) Reject the null hypothesis because the confidence interval includes the null hypothesized value.
B) Reject the null hypothesis and conclude that cleanliness did not change as a result of the manipulation.
C) Fail to reject the null hypothesis because 0 falls in the confidence interval.
D) Fail to reject the null hypothesis because the confidence interval has positive and negative values.

Question 59

What would be the decision for a two-tailed paired-samples t test where the t statistic is 2.67, with cutoffs of ±2.776?

A) reject the null hypothesis
B) fail to reject the null hypothesis
C) reject the research hypothesis
D) fail to reject the research hypothesis

Question 60

The American Psychological Association encourages researchers to report _____ for paired-samples t tests.

A) effect sizes only
B) confidence intervals only
C) both effect sizes and confidence intervals
D) either effect sizes or confidence intervals

Question 61

The paired-samples t test is also known as the dependent-samples t test.

Question 62

For the paired-samples t test, one of the assumptions is that the variance of scores at time one is similar to the variance of scores at time two, known as homogeneity of variance.

Question 63

In a paired-samples t test, a possible confounding variable that can occur as a result of the within-groups design is:

A) counterbalancing.
B) repeated measures.
C) order effects.
D) error effects.

Question 64

If the null hypothesis is true for a paired-samples t test, the mean of the distribution of mean differences is 0.

Question 65

Assume the following for a paired-samples t test: N = 12, M_difference = 467.82, s = 280.50.What is the effect size statistic?

A) 0.03
B) 0.60
C) 1.67
D) 3.34

Question 66

The effect size calculations for the paired-samples t test are interpreted in the same manner as those for the single-sample t test.

Question 67

Counterbalancing eliminates the confounding variables of within-groups designs.

Question 68

The paired-samples t test allows one to assess how performance can differ for one group of people over time.

Question 69

The equation for the paired-samples t test is the same as that for the single-samples t test except that the data are now difference scores.

Question 70

The sample mean difference should fall at the center of the confidence interval for a paired-samples t test.

Question 71

The paired-samples t test is also known as the independent-samples t test.

Question 72

For the paired-samples t test, confidence interval calculations do not add any additional information.

Question 73

One expects children's vocabularies to increase over time, with, say, 200 new words per year established as the standard.The null hypothesis for a paired-samples t test that assesses 150 children at age 5 and again at age 6 would assume an average mean difference of 200 words.

Question 74

The paired-samples t test allows one to assess how performance can differ between two groups of people over time.

Question 75

Assume the following for a paired-samples t test: N = 19, M_difference = 13.19, s = 22.3.What is the size of the effect?

A) small
B) medium
C) large
D) no effect

Question 76

A researcher is worried that performance on an aptitude test will improve simply because of repeat exposure to the instrument, which will cloud his ability to assess the impact of two unique educational interventions he wants to study.To help remove the effect of repeated exposure, the researcher could use:

A) repeated measures.
B) counterbalancing.
C) a within-groups design.
D) a single-sample t test.

Question 77

The possible threat of participants having experience with the variables in a within-groups design when they experience those variables for the second time is known as:

A) order effects.
B) counterbalancing.
C) repeated effects.
D) stimulus repeating.

Question 78

Assume the following for a paired-samples t test: N = 12, M_difference = 467.82, s = 280.50.What is the size of the effect?

A) small
B) medium
C) large
D) no effect

Question 79

One expects children's vocabularies to increase over time, with, say, 200 new words per year established as the standard.The null hypothesis for a paired-samples t test that assesses 150 children at age 5 and again at age 6 would assume an average mean difference of zero words.

Question 80

The confidence interval for a paired-samples t test is centered around a hypothesized mean difference of zero.