Deck 11: The Independent-Samples T Test

Question 1

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences.They randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training.Which statistical analysis should be performed to answer the researchers' question?

A) single-sample t test
B) z test
C) independent-samples t test
D) dependent-samples t test

Answer 1

independent-samples t test

Question 2

The mean of the comparison distribution for the null hypothesis of an independent-samples t test is:

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

Answer 2

always 0.

Question 3

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences.They randomly assigned 20 participants to a control group (no relaxation training) or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training.The independent variable in this study is:

A) training type.
B) number of headaches.
C) control group.
D) relaxation training.

Answer 3

training type.

Question 4

There are three steps involved in creating the comparison distribution for the independent-samples t test, and those steps are repeated many times.Which of these is the sequence described in the text?

A) randomly select a pair of scores, subtract the second score from the first, and record the difference between scores
B) randomly select a group of scores, calculate their mean, and plot that mean on a distribution
C) randomly select scores and calculate their mean as the group 1 mean, randomly select another group of scores and calculate their mean as the group 2 mean, and subtract the second mean from the first
D) randomly select a score, subtract the mean from the score, and plot the difference

Question 5

Mehl (2007) published in the journal Science the results of an extensive study of 396 men and women comparing the number of words uttered per day by each sex.Which statistical test should Mehl use to analyze the data?

A) single-sample t test
B) z test
C) independent-samples t test
D) dependent-samples t test

Question 6

In a(n) _____, each participant is assigned to only one group in order to compare mean differences in a between-groups design.

A) single-sample t test
B) z test
C) independent-samples t test
D) dependent-samples t test

Question 7

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences.They randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training.The dependent variable in this study is:

A) training type.
B) number of headaches.
C) control group.
D) relaxation training.

Question 8

In a(n) _____, each participant is assigned to only one group in order to compare mean differences.

A) single-sample t test
B) z test
C) independent-samples t test
D) dependent-samples t test

Question 9

Dr.Jameson wanted to know if IQ scores differed between male and female participants in his study.He gave 28 participants an IQ test and then compared IQ scores for gender differences.He hypothesized that there would be a statistically significant gender difference in IQ scores.Contrary to Dr.Jameson's hypothesis, there were no differences in IQ scores between men and women in his study.What is the independent variable in this study?

A) IQ scores
B) sample size of 28
C) gender
D) participants

Question 10

The comparison distribution for an independent-samples t test is a distribution of:

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

Question 11

Checking an independent-samples t test for the assumption of normality is part of step _____ of the six steps.

A) 1
B) 2
C) 3
D) 4

Question 12

The appropriate hypothesis test to use for a between-groups design with two groups is a(n):

A) z test.
B) paired-samples t test.
C) independent-samples t test.
D) single-sample t test.

Question 13

Unnithan, Houser, and Fernhall (2006) were interested in whether playing the game Dance Dance Revolution (DDR) affected the heart rate of overweight and non-overweight adolescents differently.A group of 22 adolescents, 10 classified as overweight and 12 as not overweight played DDR for 12 minutes, during which time the researchers measured each participant's heart rate.Which statistical test should the researchers use to analyze their data?

A) single-sample t test
B) z test
C) independent-samples t test
D) dependent-samples t test

Question 14

Dr.Jameson wanted to know if IQ scores differed between male and female participants in his study.He gave 28 participants an IQ test and then compared IQ scores for gender differences.He hypothesized that there would be a statistically significant gender difference in IQ scores.Contrary to Dr.Jameson's hypothesis, there were no differences in IQ scores between men and women in his study.Based on the information provided, does this study meet the assumption of normality? Why or why not?

A) Yes; it is normally distributed because the sample size is large.
B) No; it is not normally distributed because the small sample size is small.
C) We do not know whether it is normally distributed, and the sample size is not at least 30 participants.
D) Yes; the population is likely to be normally distributed because the sample size is less than 30.

Question 15

A clinical researcher was interested in determining whether her interventions for depression were effective in minimizing depression symptoms among her participants.To assess the effectiveness of her 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 her treatment was effective.Which statistical test was the researcher MOST likely to have used to test her hypothesis?

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

Question 16

Dr.Jameson wanted to know if IQ scores differed between male and female participants in his study.He gave 28 participants an IQ test and then compared IQ scores for gender differences.He hypothesized that there would be a statistically significant gender difference in IQ scores.Contrary to Dr.Jameson's hypothesis, there were no differences in IQ scores between men and women in his study.Which test was Dr.Jameson MOST likely to use to test his hypothesis?

A) paired-samples t test
B) z test
C) independent-samples t test
D) single-samples t test

Question 17

In a(n) _____, a within-groups design with two groups is used to compare the distribution of mean difference scores.

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

Question 18

A psychologist is interested in whether working memory is influenced by sleep loss.The psychologist administers a measure of working memory to two groups of subjects.The subjects in one group were kept awake for the entire night and the subjects in the other group maintained their normal sleep schedules.Which statistical analysis should be performed to answer the question "Does sleep loss affect working memory?"

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

Question 19

In a(n) _____, one sample is used to compare a distribution of means during hypothesis testing.

A) single-sample t test
B) z test
C) independent-samples t test
D) dependent-samples t test

Question 20

Dr.Jameson wanted to know if IQ scores differed between male and female participants in his study.He gave 28 participants an IQ test and then compared IQ scores for gender differences.He hypothesized that there would be a statistically significant gender difference in IQ scores.Contrary to Dr.Jameson's hypothesis, there were no differences in IQ scores between men and women in his study.What is the dependent variable in this study?

A) IQ scores
B) sample size of 28
C) gender
D) participants

Question 21

When statisticians describe pooling the variances, they mean:

A) adding the standard deviations of the two samples.
B) adding the variances of the two samples.
C) taking the average of the two variances, accounting for sample size.
D) taking the average of the two variances, disregarding sample size.

Question 22

The statement "On average, older adults have a different response time than younger adults" is an example of:

A) effect size.
B) statistical significance.
C) the null hypothesis.
D) the research hypothesis.

Question 23

Which of these illustrates a statistically insignificant result for an independent-samples t test?

A) t(N - 1) = 3.89, p < 0.05
B) t(15) = 3.89, p < 0.05
C) t(15) = 3.89, p > 0.05
D) t(N - 2) = 3.89, p < 0.05

Question 24

To determine the critical values or cutoffs for an independent-samples t test, use:

A) degrees of freedom for group 1.
B) degrees of freedom for group 2.
C) N - 1.
D) total degrees of freedom.

Question 25

In order to report the exact p value associated with the test statistic for an independent-samples t test, we need to:

A) use software to obtain the value.
B) record the value from the t table under the 0.05 p level.
C) compute Cohen's d.
D) record the value from the t table under the 0.01 p level.

Question 26

In an independent-samples t test, how is the research hypothesis symbolized?

A) H₁: $\mu$ ₁ $\neq$ $\mu$ ₂
B) H₀: $\mu$ ₁ $\neq$ $\mu$ ₂
C) H₁: $\mu$ ₁ = $\mu$ ₂
D) H₀: $\mu$ ₁ = $\mu$ ₂

Question 27

Dr.Jameson wanted to know if IQ scores differed between male and female participants in his study.He gave 28 participants an IQ test and then compared IQ scores for gender differences.He hypothesized that there would be a statistically significant gender difference in IQ scores.Contrary to Dr.Jameson's hypothesis, there were no differences in IQ scores between men and women in his study.From the results of the study, Dr.Jameson must _____ the null hypothesis and _____ the research hypothesis.

A) fail to reject; reject
B) reject; fail to reject
C) retest; reject
D) reject; retest

Question 28

s²_pooled is the symbol for:

A) variance.
B) pooled variance.
C) standard deviation.
D) pooled mean.

Question 29

There is(are) _____ degree(s) of freedom calculations for an independent samples t-test.

A) 0
B) 1
C) 3
D) 4

Question 30

The statement "On average, older adults have the same response time as younger adults" is an example of:

A) effect size.
B) statistical significance.
C) the null hypothesis.
D) the research hypothesis.

Question 31

_____ is a weighted average of the two estimates of _____.

A) Pooled variance; variance
B) Variance; pooled variance
C) Pooled variance; standard deviation
D) Standard deviation; pooled variance

Question 32

The formula $s _ { \text {difference } } = \sqrt { S ^ { 2 } \text { difference } }$ is used to calculate the:

A) pooled variance estimate.
B) standard deviation for an independent-samples t test.
C) squared standard error.
D) estimated standard deviation of the distribution of mean differences.

Question 33

Squared standard deviation is equivalent to the:

A) standard error.
B) variance.
C) pooled variance.
D) z test.

Question 34

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

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

Question 35

Which of these illustrates the APA format for reporting statistically significant results for an independent-samples t test?

A) t(N - 1) = 3.89, p < 0.05
B) t(15) = 3.89, p < 0.05
C) t(15) = 3.89, p > 0.05
D) t(N - 2) = 3.89, p < 0.05

Question 36

In an independent-samples t test, how is the null hypothesis symbolized?

A) H₁: $\mu$ ₁ $\neq$ $\mu$ ₂
B) H₀: $\mu$ ₁ $\neq$ $\mu$ ₂
C) H₁: $\mu$ ₁ = $\mu$ ₂
D) H₀: $\mu$ ₁ = $\mu$ ₂

Question 37

Why is it necessary to use the pooled variance when conducting an independent-samples t test?

A) We are working with two samples, and an estimate of spread based on two samples is likely to be more accurate than an estimate of spread based on a single sample.
B) It is necessary to estimate the standard deviation of the two samples in order to compare the two samples to one another.
C) Estimating the spread of the sample using the standard deviation increases the generalizability of results.
D) Using the pooled variance helps the researcher identify skewness.

Question 38

Mehl (2007) published in the journal Science the results of an extensive study of 396 men and women, comparing the number of words uttered per day by each sex.Is the population likely to be normally distributed? Why or why not?

A) Yes; the population is likely to be normally distributed because the sample size is greater than 200.
B) No; the population is not likely to be normally distributed because it has a small sample size.
C) Yes; the population is likely to be normally distributed because the sample is greater than 30.
D) We do not know whether the population is normally distributed because we do not have information on the population.

Question 39

In an independent-samples t test, the _____ is used rather than the _____.

A) standard deviation; pooled variance
B) pooled variance; standard deviation
C) standard deviation; variance
D) variance; pooled variance

Question 40

The results of an independent-samples t test were t(19) = 4.02, p < 0.05.In this example, the degrees of freedom are:

A) 0.05
B) 4.02.
C) 18
D) 19.

Question 41

A study found statistically significant results for a hypothesis tested with an independent-samples t test.The author of the study reported her effect size for the test as 0.53.What is true of the two sample means?

A) The two sample means overlap 53 percent.
B) The two sample means likely come from the same distribution.
C) The two sample means do not indicate meaningful differences between groups.
D) The two sample means are 0.53 standard deviations apart.

Question 42

The first step in calculating a confidence interval for an independent-samples t test is to:

A) look up the t statistics for the lower and upper bounds.
B) draw a normal curve.
C) write the percentages for the upper and lower bounds.
D) convert the t statistics to raw score differences between means.

Question 43

Bayesian statistics help us take into account:

A) both probabilities and future predictions.
B) only prior beliefs.
C) both prior beliefs and probabilities.
D) both prior beliefs and future predictions.

Question 44

To calculate effect size for an independent-samples t test, use:

A) Cohen's d.
B) sample size.
C) z score.
D) standard deviation scores.

Question 45

The results of an independent-samples t-test were t(19) = 4.02, p < 0.05.These results are:

A) statistically significant.
B) generalizable.
C) meaningful.
D) not statistically significant.

Question 46

The fourth step in calculating a confidence interval for an independent-samples t test is to:

A) look up the t statistics for the lower and upper bounds.
B) draw a normal curve.
C) write the percentages for the upper and lower bounds.
D) convert the t statistics to raw differences between means.

Question 47

A p level of 0.05 corresponds to a confidence interval of _____ percent.

A) 68
B) 90
C) 95
D) 99.9

Question 48

_____ statistics help us take into account both prior beliefs and probabilities.

A) Inferential
B) Nonparametric
C) Parametric
D) Bayesian

Question 49

In addition to reporting the results of statistical hypothesis testing, it is also recommended that researchers report:

A) confidence intervals and random selection results.
B) effect size and confidence intervals.
C) effect size and median differences.
D) effect size and mean difference scores.

Question 50

Which example best illustrates the APA's standards for reporting descriptive statistics for an independent-samples t test?

A) On average, men scored significantly lower (M = 4.33, SD = 0.22) compared to women (M = 6.59, SD = 0.19) on reaction time.
B) On average, men scored significantly lower ( $\mu$ = 4.33, s = 0.22) compared to women ( $\mu$ = 6.59, s = 0.19) on reaction time.
C) On average, men scored significantly lower compared to women (M = 4.33, SD = 0.22 versus M = 6.59, SD = 0.19) on reaction time.
D) On average, men scored significantly lower (X = 4.33, SD = 0.22) compared to women (X = 6.59, SD = 0.19) on reaction time.

Question 51

A p level of 0.01 corresponds to a confidence interval of _____ percent.

A) 10
B) 90
C) 95
D) 99

Question 52

A study found statistically significant results for a hypothesis tested with an independent-samples t test.The author of the study reported her effect size for the test as 0.87.According to Cohen's convention, this effect size is considered:

A) small.
B) medium.
C) large.
D) to have no overlap.

Question 53

A study found statistically significant results for a hypothesis tested with an independent-samples t test.The author of the study reported her effect size for the test as 1.24.What is true of the two sample means?

A) The two sample means overlap 85 percent.
B) The two sample means likely come from the same distribution.
C) The two sample means do not indicate meaningful differences between groups.
D) The two sample means are 1.24 standard deviations apart.

Question 54

A study found statistically significant results for a hypothesis tested with an independent-samples t test.The author of the study reported her effect size for the test as 0.18.According to Cohen's convention, this effect size is considered:

A) small.
B) medium.
C) large.
D) to have no overlap.

Question 55

Which formula for calculating the lower bound of a confidence interval is correct?

A) -t(s_difference) + (M_X - M_Y)_sample
B) t(s_mean) + (M_X - M_Y)_population
C) t(s_difference) + (M_X - M_Y)_sample
D) -t(s_mean) + (M_X - M_Y)_population

Question 56

To calculate a confidence interval for an independent-samples t test, use the:

A) difference between means.
B) difference between medians.
C) mean of the first group only.
D) mean of the second group only.

Question 57

A study found statistically significant results for a hypothesis tested with an independent-samples t test.The author of the study reported her effect size for the test as 0.60.According to Cohen's convention, this effect size is considered:

A) small.
B) medium.
C) large.
D) to have no overlap.

Question 58

Some researchers argue that Bayesian statistics should replace:

A) parametric statistics.
B) hypothesis testing.
C) nonparametric statistics.
D) confidence intervals and effect sizes.

Question 59

When calculating effect size for an independent-samples t test, _____ sample size.

A) add
B) divide by
C) disregard
D) multiply by

Question 60

Which formula for calculating the upper bound of a confidence interval is correct?

A) -t(s_difference) + (M_X - M_Y)_sample
B) t(s_mean) + (M_X - M_Y)_population
C) t(s_difference) + (M_X - M_Y)_sample
D) -t(s_mean) + (M_X - M_Y)_population

Question 61

Some researchers believe hypothesis testing should be completely replaced with Bayesian statistics.

Question 62

Pooled variance is a weighted average of the two estimates of variance from the two samples in the independent-samples t test.

Question 63

For an independent-samples t test, the test result is compared to a distribution of differences between means.

Question 64

An independent-samples t test is a _____ design.

A) between-groups
B) within-groups
C) single-samples
D) dependent-samples

Question 65

When calculating a confidence interval for an independent-samples t test, replace the population mean difference with the sample mean difference.

Question 66

When conducting an independent-samples t test, it is necessary to have an equal number of participants in both groups.

Question 67

A group of rats ran faster with a steroid drug supplement compared to a group of rats that received no steroid drug supplement.Which type of statistical test should be used to report these results?

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

Question 68

The independent-samples t test is considered a within-groups design.

Question 69

When reporting the test results for an independent-samples t test, N is reported rather than degrees of freedom.

Question 70

Why is it that the mean difference of the comparison distribution is always 0?

A) The null hypothesis posits small differences.
B) The research hypothesis posits small differences.
C) The null hypothesis posits no difference.
D) The research hypothesis always posits negative differences.

Question 71

For an independent-samples t test, the test result is compared to a distribution of means.

Question 72

Why is it necessary to use pooled variance rather than variance when conducting an independent-samples t test?

A) There are two samples.
B) It is a first step to calculating mean differences.
C) We need to remove the effects of sample size.
D) We need to multiply this value by 100.

Question 73

Bayesian statistics help us account for both prior beliefs and probabilities.

Question 74

The independent-samples t test is considered a between-groups design.

Question 75

Some researchers believe hypothesis testing should completely replace Bayesian statistics.

Question 76

The confidence interval for an independent-samples t test is an interval estimate.

Question 77

When conducting an independent-samples t test, it is not necessary to have an equal number of participants in both groups.

Question 78

When calculating a confidence interval for an independent-samples t test, replace the sample mean difference with the population mean difference.

Question 79

Bayesian statistics help us account for both prior beliefs and chance.

Question 80

Effect size cannot be calculated for the independent-samples t test.