Deck 12: The Two-Sample T-Test

Question 1

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

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

Answer 1

There is no relationship between the independent variable and the dependent variable.

Question 2

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

A)The populations of raw scores form normal distributions.
B)Their dependent scores measure an interval/ratio variable.
C)There is homogeneity of variance.
D)The standard deviation of at least one of the populations is known.

Answer 2

The standard deviation of at least one of the populations is known.

Question 3

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 3

independent samples t-test.

Question 4

What is the standard error of the difference?

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

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

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

A)sample means.
B)differences between two means when they are drawn from two raw score populations
C)differences between two means when they are drawn from one raw score population.
D)differences between two means of various sample sizes.

Question 7

What does the alternative hypothesis state in a two-tailed independent samples experiment?

A)
B)
C)
D)

Question 8

You have stated your alternative hypothesis as .If , , , ,and ,what is ?

A)2.00
B)-2.22
C)-6.09
D)Cannot be calculated from this information.

Question 9

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 10

If is true and we find a difference between our sample means,how would we explain this?

A)A relationship really does exist in the population.
B)Our samples are not independent.
C)It is likely due to sampling error.
D)We cannot explain it.

Question 11

When is true,the mean of the sampling distribution of differences between means is equal to

A)the population mean µ.
B)1.0.
C)the mean of the two sample means.
D)zero.

Question 12

What does the null hypothesis state in a two-tailed independent samples experiment?

A)
B)
C)
D)

Question 13

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 that you fail to reject the null hypothesis for this independent samples t-test.Which of the following best accounts for the difference between these sample means?

A)A math error has been made somewhere.
B)The null hypothesis was incorrect to start with.
C)The sample means probably came from different populations,and the difference is due to sampling error.
D)The sample means probably came from the same population,and the difference is due to sampling error.

Question 14

Unless otherwise specified,what is said to equal?

A)
B)1
C)0
D)

Question 15

Two samples are said to be independent when

A)we randomly select participants for a sample,without regard to who has been selected for either sample.
B)we randomly select participants for a sample,being sure to pair each person in one sample with a particular person in the other sample.
C)we randomly select participants for a sample,being sure that each participant serves in every condition of our experiment.
D)the null hypothesis of the two-sample t-test is rejected.

Question 16

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 17

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

A)0.36
B)0.71
C)0.81
D)0.85

Question 18

What is pooled variance?

A)The weighted average of the two 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 19

We know that in an independent samples t-test we could state our null hypothesis as .However,we usually state it as which of the following,instead?

A)
B)
C)
D)

Question 20

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.

Question 21

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

A)
B)
C)
D)

Question 22

There are two ways in which samples can be related.In a _____ design,each participant in one condition is paired with a participant in the other condition.In a _____ design,each participant is tested under both conditions of the independent variable.

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

Question 23

Suppose the average reading speed of 15 randomly selected elementary school students is 25,and the average reading speed of 15 randomly selected junior high school students is 31.You compute an independent samples t-test,and your is 3.12,which is statistically significant.Which of the following is the most appropriate conclusion?

A)Increases in age cause increases in reading speed.
B)We have evidence that older students tend to read faster.
C)There is a proven relationship between age and reading speed.
D)The difference between the older and younger students is due to sampling error.

Question 24

Suppose that 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.Which of the following is the most appropriate conclusion?

A)There is no relationship between length of index finger and IQ.
B)There is a relationship between length of index finger and IQ.
C)The relationship between length of index finger and IQ does not exist.
D)We do not have convincing evidence that our measured relationship between length of index finger and IQ is due to anything other than sampling error.

Question 25

What are the degrees of freedom for an independent samples t-test that uses two samples with n = 12 in each sample?

A)23
B)22
C)21
D)20

Question 26

What is the next step in an experiment if the results of an independent samples t-test are statistically significant?

A)Correlate the scores on the dependent variable with the conditions of the independent variable.
B)Compute a predicted score for each true score on the dependent variable.
C)Make a prediction about the strength of the relationship based on the scatterplot.
D)Compute a confidence interval for the difference between the $\mu$ s.

Question 27

How many subjects participated in an independent samples t-test if a researcher reports df=20 and = 3.68?

A)22
B)21
C)20
D)18

Question 28

Eighteen obese volunteers weighed themselves before and after a two-day fast.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 29

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

A)28
B)27
C)26
D)24

Question 30

For ,and ,use a and compute a 95% confidence interval for .

A)
B)
C)
D)

Question 31

How does increasing the size of the samples increase the power of an experiment?

A)Larger numbers of subjects result in smaller degrees of freedom,which results in a smaller value of .
B)Larger numbers of subjects result in larger degrees of freedom,which results in a larger value of .
C)Larger numbers of subjects result in larger degrees of freedom,which results in a smaller value of .
D)Larger numbers of subjects result in smaller degrees of freedom,which results in a larger value of .

Question 32

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

A)
B)
C)
D)

Question 33

One way to increase power is to maximize the difference produced by the two conditions in the experiment.How might this be accomplished?

A)Change $\alpha$ from 0.05 to 0.01.
B)Change the size of N from 100 to 25.
C)Design and conduct the experiment so that all the subjects in a sample are treated in a consistent manner.
D)Select two very different levels of the independent variable that are likely to produce a relatively large difference between the means.

Question 34

What are we stating if we reject the null hypothesis in an 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 significantly different from zero.
C)The sample mean difference is zero.
D)The difference between the population means is zero.

Question 35

In a related-samples design, states that

A)our population mean represents the distribution of difference scores wherein .
B)our population mean represents a sample of difference scores where .
C)our sample mean represents a population of difference scores for which .
D)our sample mean represents a population of difference scores for which .

Question 36

When are two samples considered to be related?

A)When we randomly assign participants to samples without regard to other participants selected for either sample
B)When we pair each score in one sample with a particular score in the other sample
C)When we randomly select participants to samples,making sure that each participant serves in only one condition of our experiment
D)When the null hypothesis of the two-sample t-test is retained

Question 37

The assumptions of the t-test for related samples are the same as those for the t-test for independent samples except for requiring

A)that the dependent variable be measured on an interval or ratio scale.
B)that the population represented by either sample form a normal distribution.
C)homogeneity of variance.
D)that each score in one sample be paired with a particular score in the other sample.

Question 38

One way to increase power is to minimize the variability of the raw scores.How might this be accomplished?

A)Change $\alpha$ from 0.05 to 0.01.
B)Change the size of N from 100 to 25.
C)Design and conduct the experiment so that all the subjects in a sample are treated in a consistent manner.
D)Select two very different levels of the independent variable that are likely to produce a relatively large difference between the means.

Question 39

What should you conclude if two randomly selected sample means produce a confidence interval that is ?

A)A math error was made in the computation of the interval.
B)You are 95% confident that the interval between -1.51 and 2.62 contains the difference between the $\alpha$ s for the two conditions.
C)The sample means probably came from populations with .
D)You are 95% confident that the difference between the conditions is 2.0.

Question 40

When we construct a 95% confidence interval,we are 95% sure that the

A)sample mean difference falls within the interval.
B)population mean difference falls within the interval.
C)population mean difference is at the center of the interval.
D)sample mean difference is at the center of the interval.

Question 41

If and ,what is ?

A)1.41
B)2.0
C)4.47
D)20

Question 42

On the basis of a pretest on knowledge of foreign languages,each subject in the 9:00 class was matched with a subject in the 10:30 class.The 9:00 class used a participant approach to the study of Latin,and the 10:30 class used the Hiffendorf method.At the end of the term,the same Latin test was given to both classes.The appropriate design for testing the significance of the difference between the means is

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

Question 43

Using a line graph when interpreting the results of a two-sample experiment allows us to

A)envision the scatterplot that the data would form.
B)determine the strength of the relationship.
C)see whether there are significant differences between the samples.
D)apply correlational statistics.

Question 44

When one has the option,a related-samples design should be chosen over an independent samples design because

A)related samples result in more variability,and therefore the design is more powerful.
B)related samples result in less variability,and therefore the design is more powerful.
C)related samples designs are simpler to use.
D)related samples designs are intrinsically better than independent samples designs.

Question 45

Daniel conducted an independent-samples t-test and found t(20)= 0.57,p > .05.He then calculated his effect size and obtained a value of d = 0.02.What should Daniel say in the report on his results?

A)He should indicate he has obtained a significant test result,with a small effect size.
B)He should indicate his t-test is not significant,and that his effect size is a small one.
C)He should indicate his t-test is not significant.He should,therefore,not report his effect size.
D)He should recheck his calculations because a t-value of 0.57 is not possible.

Question 46

A researcher asked 26 extroverts and 36 introverts how happy they were.The results are shown in the graph below.The = 2.96.Calculate the strength of the relationship using the squared Point-Biserial Correlation Coefficient.

A)-0.13
B)+0.13
C)-0.36
D)+0.36

Question 47

A related-samples t-test has resulted in a and .If the appropriate two-tailed ,construct a 95% confidence interval.

A)
B)
C)
D)

Question 48

Following a significant t-test,Clarinda wants to calculate her Cohen's d value.She has and .Calculate the correct Cohen's d value.

A)d = 4.00
B)d = 0.707
C)d = 0.25
D)d = 0.50

Question 49

In a related-samples t-test,if there is no treatment effect we expect will equal

A)
B)0
C)
D)

Question 50

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 51

Ten volunteers recorded their blood pressure in a room with an aquarium and then in a room without one.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 52

If ,and ,what is when and ?

A)0.63
B)2.00
C)3.16
D)Cannot be calculated from this information.

Question 53

In a related-samples t-test,we use each pair of scores to produce a D value.How is D calculated?

A)Dividing score 1 by score 2.
B)Finding the average score for each sample and then taking the difference.
C)Calculate the standard error of the means.
D)Take the difference between each pair of scores.

Question 54

In an experiment,the "proportion of variance accounted for" goes by another name.It is called the

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

Question 55

In a related-samples t-test,N equals

A)
B)The number of difference scores.
C)
D)0

Question 56

In a study to determine the effectiveness of pain management therapy in persons with chronic pain,twenty individuals experiencing chronic pain were randomly selected.Ten of these individuals were randomly assigned to receive pain management therapy and the other ten to receive no therapy.Descriptive statistics for each group are provided below.Conduct an appropriate t-test and determine the correct outcome.

A)
B)
C) 1
D)

Question 57

The nutrition class conducted a taste test in which 10 students rated the taste of regular oleo margarine and also rated the taste of fat-free oleo margarine.In a t-test for related samples, ,and .Construct a 95% confidence interval.

A)
B) 4
C)
D)

Question 58

How is the t-test for related samples performed?

A)By conducting a one-sample t-test on the sample of difference scores
B)By conducting an independent samples t-test on the sample of difference scores
C)By converting the scores to standard scores and then performing a related samples t-test
D)By measuring the population variance and testing it using an independent samples t-test

Question 59

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 $\alpha$ = 0.05.

A)1.699
B)2.042
C)2.045
D)2.048

Question 60

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

A)t(31)= 4.56;p < 0.05
B)t(29)= 4.56;p < 0.05
C)t(29)= 4.56;p > 0.05
D)t(29)= 4.56;p = 0.05

Question 61

Julius has conducted a very small study of the amount of sleep his dorm mates get each night.He believes that those who are on one of the school's sports teams will get more sleep than those who are not.Julius surveyed 12 people.Of these,6 played on a sports team and 6 did not.The descriptive statistics from his survey are given below.What is ?

A)t(5)= 2.35
B)t(5)= 2.28
C)t(10)= 1.80
D)t(10)= 1.75

Question 62

Renee is studying the effect of positive reinforcement for her psychology class.She gets 16 pigeons.These pigeons are from eight egg clutches with two pigeons from each clutch.Renee matches each pigeon in Reinforcement Schedule A with its clutchmate in Reinforcement Schedule B.After training the pigeons,she measures the number of correct responses by each in 10 trials.Using a two-tailed test and ,use the data below to determine whether or not there is a difference between the two schedules.

A)
B)
C)
D)

Question 63

Julius has conducted a very small study of the amount of sleep his dorm mates get each night.He believes that those who are on one of the school's sports teams will get more sleep than those who are not.Julius asked 6 people in his dorm who do not play sports and 6 who do play sports to participate.Because he thinks that the number of credit hours a student is taking also might impact sleep habits,he matched each person in the "plays sports" group with a person in the "does not play sports" group who was carrying the same number of hours.The descriptive statistics from his survey are given below.Conduct an appropriate one-tailed t-test using and determine the t_obt.

A)t(5)= 2.35
B)t(5)= 2.28
C)t(10)= 1.80
D)t(10)= 1.75

Question 64

In a study to determine the effectiveness of pain management therapy in persons with chronic pain,20 individuals experiencing chronic pain were selected.Based on each individual's assessment of his or her pain level,each participant in the group that received the therapy was matched with a participant in the group that did not receive the therapy.Descriptive statistics regarding the differences in scores are provided below.Conduct an appropriate two-tailed t-test for using and determine the appropriate outcome.

A)
B)
C)
D)

Question 65

Renee is studying the effect of positive reinforcement for her psychology class.She randomly assigns 16 pigeons to two different positive reinforcement schedules.After training the pigeons,she measures the number of correct responses by each in 10 trials.Using a two-tailed test and ,use the data below to determine whether or not there is a difference between the two schedules.

A)
B)
C)
D)