Deck 9: Hypothesis Testing Using the Two-Sample T-Test

Question 1

The first 10 students who arrived for the Friday lecture filled out a questionnaire on their attitudes toward the instructor.The first 10 who were late for the lecture were spotted, and afterward filled out the same questionnaire. The appropriate design for testing the significance of the difference between the means is

A)related-samples t-test.
B)independent-samples t-test.
C)one-sample t-test.
D)z-test.

Answer 1

B

Question 2

The freshmen competed with the sophomores to see who could raise the most money by recycling.The appropriate design for testing the significance of the difference between the means is

A)related-samples t-test.
B)independent-samples t-test.
C)one-sample t-test.
D)z-test.

Answer 2

B

Question 3

By convention, the mean of the sampling distribution equals

A)0.
B)the mean of the sample.
C)1.
D)-1.

Answer 3

A

Question 4

Eighteen overweight volunteers weighed themselves before and after a two-week diet.The appropriate design for testing the significance of the difference between the means is

A)related-samples t-test.
B)independent-samples t-test.
C)one-sample t-test.
D)z-test.

Question 5

At a card players' club, the poker players had a contest with the blackjack players to see who could win the most money.The appropriate design for testing the significance of the difference between the means is

A)related-samples t-test.
B)independent-samples t-test.
C)one-sample t-test.
D)z-test.

Question 6

What does the homogeneity of variance assumption state?

A)The two sample variances are equal.
B)The population variance is equal to the variance of the sample selected from it.
C)The variance must stay constant for each subject in the experiment.
D)The variance in one population is equal to the variance in the other population.

Question 7

What can we conclude if we reject the null hypothesis in an independent-samples t-test?

A)It is likely that sampling error accounted for the differences between the sample means.
B)It is likely that the sample means came from the same population.
C)The difference between our sample means is unlikely to be representing zero difference in the population means.
D)The difference between our sample means is merely a poor representation of zero difference in the population means.

Question 8

What does the independent-samples t-test determine?

A)It determines the probability of obtaining the observed difference between $\bar{X}_{1}$ and $\bar{X}_{2}$ when $H_{0}$ is true.
B)It determines your ? level.
C)It determines how far ?₁ is from ?₂.
D)It determines how far $\bar{X}_{1}$ is from $\bar{X}_{2}$ .

Question 9

What is the standard error of the difference?

A)The standard deviation of the sample means
B)The standard deviation of the sampling distribution of the mean
C)The standard deviation of the sampling distribution of differences between means
D)The pooled standard deviation from the populations from which the samples are drawn

Question 10

In a study involving stress among college students, a group of seniors are asked to complete a stress survey.After a two-hour seminar on relaxation methods, they are asked to complete the stress survey again.The appropriate design for testing the significance of the difference between the means is

A)related-samples t-test.
B)independent-samples t-test.
C)one-sample t-test.
D)z-test.

Question 11

The freshmen competed with the sophomores to see who could raise the most money by recycling.Each freshman was paired with a sophomore of the same gender.The appropriate design for testing the significance of the difference between the means is

A)related-samples t-test.
B)independent-samples t-test.
C)one-sample t-test.
D)z-test.

Question 12

In an experiment, the "proportion of variance accounted for" is also called the

A)effect size.
B)error reduction coefficient.
C)confidence interval.
D)standard error of the difference between means.

Question 13

How is the null hypothesis of the independent-samples t-test verbalized?

A)There is a difference between the means for the two conditions of the independent variable.
B)There is no difference between the means for the two conditions of the independent variable.
C)The difference between the sample means is equal to μ.
D)The independent variable has an effect on the dependent variable.

Question 14

How is the proportion of variance accounted for calculated?

A)It is the same as the point-biserial correlation coefficient.
B)It is the square root of the point-biserial correlation coefficient.
C)It is the squared point-biserial correlation coefficient.
D)It is the slope and intercept of the regression line.

Question 15

What are we stating if we reject the null hypothesis for the independent-samples t-test?

A)The sample mean difference represents no difference between two population μs.
B)The sample mean difference represents a difference between two population μs that is not zero.
C)The sample mean difference is zero.
D)The difference between the population means is zero.

Question 16

To determine the extent to which the conditions of the independent variable determine dependent scores, we should compute

A)the effect size.
B)an independent-samples t-test.
C)a related-samples t-test.
D)the standard error of the difference between means.

Question 17

The sampling distribution of differences between means is the distribution of all possible

A)sample means.
B)differences between two means.
C)differences between two means when drawn from the raw score populations described by .
D)differences between two means when drawn from the raw score populations described by .

Question 18

N represents _____, whereas n represents _____.

A)the total number of scores in the study; the number of scores in each sample
B)the number of scores in each sample; the total number of scores in the study
C)the number of pairs in the study; the number of difference scores in the study
D)the number of difference scores in the study; the number of pairs in the study

Question 19

Which of the following is not one of the assumptions of the t-test for independent samples?

A)The populations of raw scores form at least a roughly normal distribution.
B)There are two independent samples of interval/ratio scores.
C)There is homogeneity of variance.
D)The standard deviation of at least one of the populations is known.

Question 20

What is pooled variance?

A)The weighted average of the sample variances
B)The variance of the difference between the sample means
C)The sum of the two sample variances
D)The variance of the populations from which the samples were drawn

Question 21

If a researcher predicts the experimental treatment will produce an decrease in an independent-samples t-test
, how will the alternative hypothesis be stated?

Question 22

Suppose you measure the IQ of 14 subjects with short index fingers and the IQ of 14 subjects with long index fingers.You compute an independent-samples t-test, and the is 0.29, which is not statistically significant.What is the most appropriate conclusion?

Question 23

If a researcher predicts the experimental treatment will produce an increase in an independent-samples t-test
, how will the null hypothesis be stated?

Question 24

When is true, what does the mean of the sampling distribution of differences between means equal?

Question 25

Suppose the average reading speed of 15 randomly selected elementary school students is 25, and the average reading speed of 15 randomly selected middle school students is 31.You compute an independent-samples t-test, and your is 5.72, which is statistically significant.What is the most appropriate conclusion?

Question 26

A Cohen's d value of .5 would be viewed as indicative of a effect.

A)medium
B)small
C)large
D)very large

Question 27

In order to find the t-obtained for an independent t-test, which step is not required?

A)Set up the sampling distribution
B)Compute the pooled variance
C)Compute the standard error of the difference
D)Determine the means of your groups

Question 28

If = 20, N = 10, and = 4, what is when and ?

Question 29

State the null hypothesis for a two-tailed independent samples experiment.

Question 30

What are the degrees of freedom for an independent-samples t-test using one sample with n = 13 and one sample with n = 15?

Question 31

If a researcher predicts the experimental treatment will produce an increase in an independent-samples t-test , how will the alternative hypothesis be stated?

Question 32

You have stated your alternative hypothesis as .If = 23, = 25, = 15, = 15, and
= 0.90, what is ?

Question 33

Suppose a researcher assessed attitudes towards a certain brand of soda before and after conducting a taste test and noted the following results: $\begin{array}{ll}\text { Pre } & \text { Post } \\5 & 7 \\4 & 9 \\3 & 4 \\5 & 10 \\4 & 4 \\5 & 4\end{array}$ What is the mean difference?

A)-2
B)-12
C)12
D)6

Question 34

If = 20, = 220, and N = 10, what is ?

Question 35

Suppose a researcher compares 50 pairs of husbands and wives on a variety of attitudes.In doing so, the researcher is making use of _________________ samples with a ______________________ design.

A)related; matched-samples
B)related; repeated measures
C)independent; matched-samples
D)independent; repeated measures

Question 36

An appropriate example of a repeated measures design would be

A)comparing individual attitudes about drinking before and after viewing a film on the topic.
B)contrasting how the personalities of identical twins may differ.
C)ascertaining whether a given sample is a good representative of a given population.
D)comparing how men and women differ on memory tasks.

Question 37

Suppose you tested two age groups on the number of details they could recall from a paragraph.The mean for the older group is 16, and the mean for the younger group is 14.Further suppose you fail to reject the null hypothesis for this independent-samples t-test.What best accounts for the difference between these sample means?

Question 38

What are the degrees of freedom for an independent-samples t-test using two samples with n = 20 in each sample?

Question 39

How many subjects participated in an independent-samples t-test if a researcher reports t20) = 3.68?

Question 40

If a researcher predicts the experimental treatment will produce a decrease in an independent-samples t-test
, how will the null hypothesis be stated?

Question 41

Suppose your t-obtained is 3.13 with 18 degrees of freedom.What is the squared point-biserial correlation coefficient?

Question 42

Suppose at a given high school, juniors and seniors who participate in a certain sport are paired according to their athletic ability and then comparisons of their GPA are made.What type of research design is this and why?

Question 43

Is a significant result also important? Briefly explain.

Question 44

Suppose you read in a journal article, t43)= -3.31, p <.05.What would N be if this was an independent- versus a related samples t-test?

Question 45

Suppose you want to do an independent-samples t-test where you have 60 subjects in one group and 53 in the other group.Are the unequal ns problematic?

Question 46

Suppose you perform a two-tailed independent-samples t-test, using α = 0.05, with 15 participants in one group and 16 participants in the other group.Your is 4.56, which is significant.What is the correct way to report this finding?

Question 47

When calculating Cohen's d, how does the numerator differ from an independent-samples test versus a related samples t-test?

Question 48

If the variance for Sample 1 is 5 and the variance for Sample 2 is 3, where = 10 and = 12, what is ?

Question 49

For a study with a related samples design and 30 participants in which each participant is measured twice repeated measures), what is the critical value? Assume a two-tailed test with α = .05.