Deck 8: The T Test for Independent Means

Question 1

In which of the following situations would a t test for independent means be conducted?

A)a comparison of the SAT scores of a group of 10 students who completed a special SAT preparation course compared to the scores of students in general on the SAT
B)a comparison of scores of participants in a memory study where one group is assigned to learn the words in alphabetical order and another group is assigned to learn the words in order of length of the word
C)a comparison of participants' scores on a skills test before and after attending a training session intended to improve the skill
D)a comparison of participants' logical reasoning skills with the general population

Answer 1

a comparison of scores of participants in a memory study where one group is assigned to learn the words in alphabetical order and another group is assigned to learn the words in order of length of the word

Question 2

A "distribution of differences between means" can be thought of as a distribution of

A)difference scores,which are found by subtracting sample means from the population mean.
B)the differences obtained when several methods of estimating the population mean are used in sequence.
C)the differences obtained when a sample mean from one population is repeatedly subtracted from a sample mean from another population.
D)the differences between a single sample from Population 1 and all possible samples from Population 2.

Answer 2

the differences obtained when a sample mean from one population is repeatedly subtracted from a sample mean from another population.

Question 3

In the formula,S²_difference = S²_M1 + S²_M2,the "S²_M1" is

A)the estimated mean of the distribution of variances of Population 1.
B)the variance of the difference scores for Population 1.
C)the estimated variance of Population 1.
D)the variance of the distribution of means for Population 1.

Answer 3

the variance of the distribution of means for Population 1.

Question 4

The best way to reduce the variances in the distributions of means when conducting a t test for independent means is to

A)increase the size of the samples.
B)raise the study's level of significance.
C)use the true population variance.
D)treat the two samples as one sample.

Question 5

The variance of a distribution of differences between means is equal to

A)the difference between the variances of the two distributions of means.
B)the sum of the variances of the two distributions of means.
C)the difference between the two estimated population variances.
D)the sum of the two estimated population variances.

Question 6

Which statement is only true for the t test for dependent means rather than t tests in general?

A)Population variances are estimated from the information in the sample of scores actually studied.
B)Pretest-posttest experimental designs are common.
C)The population means are unknown.
D)The sample scores (in some form)are compared to a t distribution.

Question 7

A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows.
What is the pooled estimate of the population variance?

A)[(14 / 36)(6.5)] + [(22 / 36)(4.5)] = 5.28
B)[(15 / 38)(6.5)] + [(23 / 38)(4.5)] = 5.29
C)[(15 / 23)(6.5)] + [(23 / 15)(4.5)] = 11.14
D)[(14 / 22)(6.5)] + [(22 / 14)(4.5)] = 11.21

Question 8

When figuring the pooled population variance estimate in a t test for independent means,

A)the variance of at least one of the original populations must be known,as opposed to estimated,but the other can be estimated from sample scores.
B)the variance of BOTH of the original populations must be known,as opposed to estimated.
C)the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
D)the scores from both samples are combined to form a single sample,and the estimated variance is figured in the usual way using this combined sample.

Question 9

If an experimenter conducts a t test for independent means and rejects the null hypothesis,the correct interpretation is that

A)the samples were from populations that were actually dependent rather than independent.
B)the variance of one sample is so much larger than the variance of the other sample that the variances of the parent populations must not have been the same after all.
C)the mean of one sample is so far from the mean of the other sample that the samples must come from populations with different means.
D)the mean of one sample is statistically the same as the mean of the other sample,so they probably come from populations with equal means.

Question 10

The mean of a distribution of differences between means is equal to

A)0
B)1
C)the difference between the sample means
D)the weighted average of the sample means

Question 11

A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows.
If a t test for independent means is conducted,how many degrees of freedom will be used to locate the cutoff score in the t table?

A)(15 - 1)+ (23 - 1)= 36
B)15 + 23 = 38
C)(15 + 23)- 1 = 37
D)(15 + 23)/ 2 = 19

Question 12

In the formula,t = (M₁ - M₂)/ S_difference,"S_difference" is

A)the sum of the standard deviations of the distribution of means.
B)the pooled estimate of the populations' standard deviation.
C)the standard deviation of the distribution of differences between means.
D)the average standard deviation of the two samples.

Question 13

The comparison distribution for a t test for independent means is a t distribution instead of a normal curve because

A)tables are not available for the normal curve.
B)the population variance is estimated.
C)Z distributions were not used at the time the t test for independent means was invented.
D)there are more degrees of freedom for two samples than for one.

Question 14

When conducting a t test for independent means,a typical research hypothesis might be

A)the mean of Population 1 is greater than the mean of Population 2.
B)the mean of Sample 1 is greater than the mean of Sample 2.
C)the mean of Population 1 is the same as the mean of Population 2.
D)the mean of Sample 1 is the same as the mean of Sample 2.

Question 15

Based on the following results,which would be the correct use of the formula,t = (M₁ - M₂)/ S_difference?
Sample 1: Mean = 60; Variance of the distribution of means = 2
Sample 2: Mean = 50; Variance of the distribution of means = 7

A)t = (7 - 2)/ √(50+60)
B)t = (60 - 50)/ √(2²+7²)/2
C)t = (60 - 50)/ √(2+7)
D)t = (60 - 50)/ (2+7)

Question 16

When conducting a t test for independent means,once the variances are known for each of the distributions of means,the variances can be added together to give the

A)pooled estimate of the population variance.
B)variance of the distribution of differences between means.
C)t score.
D)power of the study.

Question 17

An experimenter hypothesizes that biology majors score higher than literature majors on an intelligence test.If the mean score for biology majors was 18.8 and the mean score for literature majors was 21.3,and the S_difference was 0.9,the t score was

A)t = (18.8 - 21.3)/ 0.9² = -3.09
B)t = (18.8 - 21.3)/ 0.9 = -2.78
C)t = (18.8 - 21.3)(0.9)= -2.25
D)t = (18.8 - 21.3)/ [(2)(0.9)] = -1.39

Question 18

When using a t table,the degrees of freedom used for a t test for independent means is

A)the degrees of freedom for sample 1,divided by the sum of the degrees of freedom for both samples.
B)the average of the degrees of freedom for the two samples.
C)the sum of the two sample sizes,minus one.
D)the sum of the degrees of freedom for the two samples.

Question 19

A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows.
If the standard deviation of the distribution of the difference between means is 0.76,what is the t score?

A)(15 - 23)/ 0.76 = -10.53
B)(0.76)(15 - 23)= -6.08
C)[(6.5 + 4.5)/ 2] [0.76] = 4.18
D)(55 - 51)/ 0.76 = 5.26

Question 20

The comparison distribution for a t test for independent means is a

A)distribution of differences between means.
B)Z distribution (that is,a normal curve).
C)poisson distribution.
D)distribution of proportional variance scores.

Question 21

"Monte Carlo" methods

A)are often used to test the effect of violating assumptions of statistical tests.
B)have been used primarily to create new statistical methods,including the t test for independent means.
C)were invented by Egon Pearson.
D)were invented by "Student" (Gossett).

Question 22

You plan to conduct a study where your nondirectional hypothesis will be assessed with a t test for independent means at the .05 significance level.If you are predicting a large effect size,how many participants would you need in total (assuming equal Ns per group)to obtain 80% power?

A)20
B)26
C)40
D)52

Question 23

Which of the following assumptions does not apply to the t test for independent means?

A)homogeneity of variance.
B)independence of scores.
C)normally distributed populations.
D)unweighted averages.

Question 24

The results of a t test for independent means can be misleading when the sample variances are

A)not at all different (e.g.,a 1 : 1 ratio).
B)a little different (e.g.,a 1.5 : 1 ratio).
C)moderately different (e.g.,a 2 : 1 ratio).
D)very different (e.g.,a 4 : 1 ratio).

Question 25

When carrying out a t test for independent means

A)the medians of the two populations are assumed to be equal.
B)the null hypothesis is rejected if the computed t score is more extreme than the cutoff t score.
C)only the .01 significance level should be used because of the greater power compared to a t test for dependent means.
D)only the .10 significance level should be used because of the assumption that the variances of the two distributions should be equal.

Question 26

Assuming that the difference between two independent sample means is 6.24,and S²_difference = 27,what is the calculated t score?

A)(6.24 + 2)/ 27 = 0.31
B)(6.24 + 2)/ √27 = 8.24 / 5.20 = 1.58
C)6)24 / 27 = 0.23
D)6)24 / √27 = 6.24 / 5.20 = 1.20

Question 27

Which of the following statements is true if a study measures two groups on each of 27 variables,and the experimenter carries out a t test for independent means for each variable (that is,27 t tests)using the .05 significance level?

A)If any of the t tests are significant,there is clearly a difference between groups on all variables at the overall .05 level.
B)It is not proper to carry out any t tests in this situation.
C)The chance of a Type II error is high.
D)The chance of at least one t test being significant is greater than 5%.

Question 28

Advanced topic: The value of the harmonic mean

A)is disproportionately influenced by smaller numbers (meaning,smaller sample sizes).
B)is disproportionately influenced by larger numbers (meaning,larger sample sizes).
C)is equidistant from both group sizes.
D)cannot be determined without more information.

Question 29

A t test for independent means is reported as "t (28)= 4.21,p < .01." This means

A)the result is not statistically significant.
B)there were 28 participants in the study.
C)the t score was 4.21.
D)the power was high.

Question 30

Advanced topic: If a study has 18 participants in the experimental group and 7 in the control group,what is the harmonic mean?

A)18/(18+7)+ 7/(18+7)= 1.00
B)(2)(18)/(18+7)+ (2)(7)/(18+7)= 2.00
C)(2)(18)(7)/ (18+7)= 10.08
D)(18+7)² / (18+7)= 25

Question 31

Which of the following tactics will reduce the power of a planned study using a t test for independent means?

A)using a less stringent significance level (such as .10 instead of .05)
B)using more precise measures
C)increasing the size of your samples
D)using unequal sample sizes instead of equal ones (for the same number of participants)

Question 32

You plan to conduct a study where your directional hypothesis will be assessed with a t test for independent means at the .05 significance level.If you are predicting a medium effect size,how many participants would you need in total (assuming equal Ns per group)to obtain 80% power?

A)50
B)64
C)100
D)128

Question 33

You plan to conduct a study where your directional hypothesis will be assessed with a t test for independent means at the .05 significance level.Assuming that you will recruit 50 participants per group and predict a small effect size,how much power will your study have?

A).17
B).26
C).29
D).41

Question 34

Which of the following is the MOST serious violation of an assumption for the t test for independent means?

A)The sample size is smaller than 15.
B)The populations are both dramatically negatively skewed.
C)The populations are both dramatically positively skewed.
D)The populations are dramatically skewed in opposite directions.

Question 35

You conducted a t test for independent means,and found that the t score equaled 0.This means that

A)the two population means must be equal.
B)the two population variances must be equal.
C)the two sample means must be equal.
D)the two sample variances must be equal.

Question 36

In an experiment with 50 participants,which division of participants into groups would have the most power?

A)15 experimental,35 control
B)40 experimental,10 control
C)25 experimental,25 control
D)all divisions would have the same power

Question 37

Advanced topic: If a study has 18 participants in the experimental group and 7 in the control group,the harmonic mean will be closest to a value of

A)5
B)7
C)18
D)25

Question 38

You plan to conduct a study where your nondirectional hypothesis will be assessed with a t test for independent means at the .05 significance level.Assuming that you will recruit 20 participants per group and predict a medium effect size,how much power will your study have?

A).33
B).46
C).60
D).72

Question 39

One of the assumptions for the t test for independent means is that

A)sample means are not significantly different.
B)the mean of the distribution of differences between means is 1.
C)the variance of each of the parent populations is the same.
D)the mean of each of the parent populations vary by no more than 1 standard deviation.

Question 40

The most common way for a t test for independent means to be reported in a research article is

A)t (i:29)< .05
B)independent t (15): 30,p: significant
C)t (independent)= 2.9,significant
D)t (45)= 3.5,p < .05

Question 41

The shape of the distribution of differences between means will be __________.

Question 42

To conduct a t test for independent means,the populations should both be normally distributed and have the same __________.

Question 43

In a t test for independent means,once the two estimates of the population variance have been computed,the next step is to combine them to form a(n)__________.

Question 44

Since a t test for independent means may be used when Sample 1 and Sample 2 include different numbers of participants,the two estimates of the population variance are combined into an overall pooled estimate using a(n)__________.

Question 45

When conducting a t test for independent means,a typical null hypothesis is that the mean of Population 1 equals the mean of __________.

Question 46

The hypothesized effect size (d)for a study involving a t test for independent means is the difference between the hypothesized population means divided by __________.

Question 47

The standard t test for independent means should not be used if the populations are highly __________ in opposite directions.

Question 48

The denominator in the effect size formula for the t test for independent means is __________.

Question 49

Assuming that the difference between two independent sample means is 6.24,and S²_difference = 27,the calculated t score should be __________.

Question 50

When the "independent scores" assumption of the t test for independent means is violated,the researcher should __________.

Question 51

If a psychologist interested in the effects of smell on concentration has 20 participants perform a standard task while exposed to an unpleasant smell and another 20 participants perform the same task without being exposed to the unpleasant smell,the appropriate test to analyze the data is a t test for __________.

Question 52

If an experimenter were to subtract a mean from one population's distribution of means and subtract it from a mean from another population's distribution of means a large number of times,the resulting distribution would be a(n)__________.

Question 53

df₁ + df₂ = __________.(Give a symbol.)

Question 54

If 15 participants take a creativity test twice,once in a normal mental state and once under the influence of an experimental drug,the appropriate test to analyze the data is a t test for __________.

Question 55

When calculating a t test for independent means,the difference between the means of the two samples is divided by the standard deviation of __________ to give the t score.

Question 56

Even if the population variances are somewhat different,the t test for independent means would probably still be accurate because this test is __________ to violations of the assumption of equal population variances.

Question 57

"S²_pooled / N₁" is the formula to find the variance of the __________ for Population 1.

Question 58

The symbol "S²_M2" represents __________.

Question 59

"t = (M₁ - M₂)/ S²_difference" is the formula for a(n)__________.

Question 60

"t = (M - μ)/ S_M" is the formula for a(n)__________.

Question 61

A theater arts department enlisted the help of a social psychology professor to design a study to see if being surrounded by highly attractive people affected the performance of young actors.Thirty student actors were randomly assigned to act a particular scene under one of two conditions: For 13 of the actors,the other performers were dressed and made up to look very attractive; for the other 17 actors,the other performers were dressed and made up to look very unattractive.A panel of judges rated the performance of the two groups,and the mean performance ratings for the actors with attractive co-performers was 4.3 (S = .86)and with unattractive co-performers,the mean was 5.4 (S = 1.30).Using the .05 significance level,did acting with attractive co-performers affect performance?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.

Question 62

Advanced topic: The statistic used to determine the power of a t test for independent means when the sample sizes are unequal is the __________.

Question 63

Assuming the null hypothesis is true in each case,if the results of 100 studies are analyzed,each using the .01 significance level,on average __________ will be significant.(Give a number.)

Question 64

A psychologist obtained recordings of election-night acceptance speeches of seven newly elected representatives to the U.S.Congress and counted the number of minutes devoted to urban problems in these speeches.The four of these representatives from rural districts devoted 5,0,3,and 4 minutes to urban problems,and the three representatives from urban districts devoted 11,11,and 14 minutes to urban problems.Using the .05 significance level,did the amount of time devoted to urban problems in the acceptance speech differ according to the type of district the representative represented?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.

Question 65

A health psychologist conducted an experiment in which participants watched a film that either did or did not include a person being injured because of not wearing a seat belt.A week later,as part of a seemingly different study,these same participants reported how important they thought it was to wear seat belts.The 22 participants who had seen the injury film gave a mean rating of 8.3,with an estimated population standard deviation of 1.6.The 30 participants in the control condition had a mean of 7.4 with an estimated population standard deviation of 2.2.Using the .01 significance level,does seeing a movie where a person gets injured due to not wearing a seat belt make attitudes more positive towards seat belt usage as indicated by higher ratings?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.

Question 66

In an experiment with 48 participants,a small effect size is most likely to be detected if the experimenter assigns __________ participants to the experimental group and __________ participants to the control group.(Give numbers.)

Question 67

A forensic psychologist conducted a study to examine whether being hypnotized during recall affects how well a witness can remember facts about an event.Nine participants watched a short film of a mock robbery,after which each participant was questioned about what he or she had seen.The five participants in the experimental group were questioned while they were hypnotized and gave 14,18,13,20,and 10 accurate responses.The four participants in the control group gave 16,20,17,and 19 accurate responses.Using the .05 significance level,do hypnotized witnesses perform differently than witnesses who are not hypnotized?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.

Question 68

A manager of a small store wanted to discourage shoplifters by putting signs around the store that said,"Shoplifting is a crime!",while at the same time making sure the signs would not reduce the number of sales.To test the effect on sales,the signs were displayed every other Wednesday for 8 weeks,and the numbers of sales for those four Wednesdays were 83,73,81,and 79.The numbers of sales for the four alternate Wednesdays without the sign were 84,90,82,and 84.Using the .05 significance level,did customers make fewer purchases when the signs were displayed?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.

Question 69

A team of cognitive psychologists studying the effects of sleep deprivation on short-term memory decay had eight participants stay in a sleep lab for two days.Four participants were randomly assigned to a condition in which they were not permitted to sleep during that period,while the other four participants were allowed to sleep when they wanted to.At the end of the two days,the participants completed a short-term memory task that yielded the results in the table that follows.Using the .05 significance level,did sleep deprivation reduce short-term memory? a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.

Question 70

The computer-based procedures statisticians use to evaluate how well statistical tests like the t test for independent means hold up when their assumptions are violated by making many repeated computations using random numbers are called __________.

Question 71

The standard way of describing the results of a study with two groups of 10 participants each and a t of 2.21 obtained using a t test for independent means that was significant at the .05 significance level in a research article would be __________.

Question 72

A consumer psychologist who wanted to know if customers really are influenced to buy more by sales clerks who smile more gave special instructions to clerks at eight stores in a large Canadian clothing chain at the start of a week and recorded sales for the week.Clerks in four of the randomly selected stores received instructions to be especially courteous and to be sure to smile a lot.Clerks at four other stores were simply instructed to be especially courteous.Sales (in thousands of dollars)for the four stores in the Smile condition were 36,40,36,and 44; sales for the four stores in the control condition were 40,31,27,and 30.Using the .05 significance level,do customers buy more from smiling sales clerks?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Figure the effect size.
d.Explain the logic of what you did to a person who is familiar with the t test for a single sample,but who is unfamiliar with the t test for independent means.Be sure you explain how this problem differs from a t test for a single sample.Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.