Deck 9: The T Test for Independent Means

Question 1

Consider a study in which the population variance estimate based on an experimental group of 10 participants is 70, and the population variance estimate based on a control group of 20 participants is 50. Compute the pooled estimate of population variance.

A)48.6
B)56.4
C)61.3
D)65.4

Answer 1

56.4

Question 2

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 deviations
C)the standard deviation of the distribution of differences between means
D)the average standard deviation of the two samples

Answer 2

the standard deviation of the distribution of differences between means

Question 3

All of the following are true for both the t test for independent means AND the t test for dependent means, EXCEPT:

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 eventually compared to a t distribution

Answer 3

pretest-posttest experimental designs are common

Question 4

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)/ 4 + 49
C)t = 60-50 / 3
D)t = 60-50 / 9

Question 5

You conduct a t test for independent means and reject the null hypothesis. This means 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 you decide that the variances of the parent populations must not have been the same
C)the mean of one sample is so far from the mean of the other sample that you decide 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 6

In a t test for independent means, the weighted average of the estimates of the population variance from two samples is known as the:

A)estimate of sample standard deviation
B)primed estimate of population standard deviation
C)pooled estimate of population variance
D)pooled estimate of degrees of freedom

Question 7

Consider a study in which the population variance estimate based on a treatment group of 14 participants is 8, and the population variance estimate based on a control group of 17 individuals is 9. Compute the pooled estimate of population variance.

A)8)55
B)9)22
C)10. 05
D)11.11

Question 8

The variance of a distribution of differences between means equals:

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 standard deviations

Question 9

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

A)distribution of differences between means
B)Z distribution (i.e., a normal curve)
C)distribution of difference scores
D)distribution of proportional variance scores

Question 10

When using a t table, the degrees of freedom you should use for a t test for independent means is the:

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

Question 11

In the formula" = S²M₁ + S²M₂" the "S²M₁" 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 standard deviation of Population 1
D)the variance of the distribution of means for Population 1, based on an estimate of the population variance

Question 12

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 13

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

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 14

The comparison distribution for a t test for independent means is a t distribution (as opposed to 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 a single sample than for when you use two samples

Question 15

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

A)difference scores, in which the difference scores are found by subtracting a series of sample means from the population mean
B)the differences you find when you use several methods, in sequence, of estimating the population mean
C)the differences you get when you repeatedly draw a sample mean from one population and a sample mean from another population and subtract one mean from the other
D)the differences between a single sample from Population 1 and all possible samples from Population 2

Question 16

Which of the following is an example of a situation in which you could conduct a t test for independent means?

A)A comparison of the SAT scores of a group of 10 students who completed a special SAT preparation course compared to how people do on the SAT in general.
B)A comparison of scores of participants in a memory study in which one group learns the words in alphabetical order and another group learns the words in order of word length.
C)A comparison of participants' scores on a skills test before and after attending a training session for improving the skill.
D)None of the above would be suitable for a t test for independent means.

Question 17

In a t test for independent means, the square root of the variance of distribution of differences between means is known as the:

A)overestimate of population variance
B)pooled estimate of population standard deviation
C)variance of the distribution of differences between means
D)standard deviation of the distribution of differences between means

Question 18

The __________ is a hypothesis-testing procedure in which there are two separate groups of people tested and the population variance is not known.

A)t test for dependent means
B)t test for a single sample
C)t test for independent means
D)t test for repeated measures

Question 19

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 Sample 1 is the same as the mean of Sample 2
D)the mean of Population 1 is the same as the mean of Population 2

Question 20

When determining 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, but using this combined sample

Question 21

Cohen's conventions for the t test for independent means are approximately __________ for a small effect size, __________ for a medium effect size, and __________ for a large effect size.

A) .1, .3, .5
B)2, 4, 6
C) .2, .5, .8
D)3, 6, 9

Question 22

For a study using a t test for independent means, with any given total number of participants, power is greatest when the participants are divided into __________ groups.

A)2 equal
B)3 equal
C)2 unequal
D)3 unequal

Question 23

In a t test for independent means, when the number of scores in the two groups differs, the __________ is used as the equivalent of each group's sample size when determining power.

A)power coefficient
B)pooled estimate
C)harmonic mean
D)independent t scores

Question 24

Each of the following is part of conducting a t test for independent means, EXCEPT:

A)difference scores are found for each participant
B)the population variances are estimated
C)a comparison is made against a t distribution
D)the variance of the distribution of differences between means is figured

Question 25

For the following question(s): A sociologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index (high scores mean high degrees of approval of one's social role). The results were as follows:
Ethnic Group A: N = 15 M = 55 S² = 6.5
Ethnic Group B: N = 23 M = 51 S² = 4.5
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 26

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

A)the 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 two parent populations is the same
D)the means of each of the two parent populations vary by no more than 1 SD

Question 27

For the following question(s): A sociologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index (high scores mean high degrees of approval of one's social role). The results were as follows:
Ethnic Group A: N = 15 M = 55 S² = 6.5
Ethnic Group B: N = 23 M = 51 S² = 4.5
If the standard deviation of the distribution of the difference between means is .76, what is the t score?

A)(15-23)/.76 = -10.53
B)()76)(15-23)= -8.00
C)[(6.5 + 4.5)/2][.76] = 4.18
D)(55-51)/.76 = 5.26

Question 28

Suppose you carry out a study using a t test for independent means. The number of participants in each group is 40 and you conduct a one-tailed test. What would be the approximate level of power if you anticipated a medium effect size? (Consult the power table 9-4.)

A) .07
B) .72
C) .97
D) .29

Question 29

When conducting a t test for independent means:

A)you assume the medians of the two populations are equal
B)you reject the null hypothesis if the t score is more extreme than the cutoff t score
C)you should use only the .01 significance level because of the greater power compared to a t test for dependent means
D)all of the above

Question 30

Many computer programs provide two sets of results for the t test for independent means. The standard method assumes that the population variances are __________ ; an alternative procedure takes into account that the population variances may be __________.

A)negatively skewed; positively skewed
B)skewed; normally distributed
C)equal; unequal
D)divisible by one another; highly skewed

Question 31

Suppose you carry out a study using a t test for independent means. The number of participants in each group is 50 and you conduct a two-tailed test. What would be the approximate level of power if you anticipated a small effect size? (Consult the power table 9-4.)

A) .53
B) .80
C) .60
D) .17

Question 32

For the following question(s): A sociologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index (high scores mean high degrees of approval of one's social role). The results were as follows:
Ethnic Group A: N = 15 M = 55 S² = 6.5
Ethnic Group B: N = 23 M = 51 S² = 4.5
If you conduct a t test for independent means, how many degrees of freedom are in the t distribution?

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

Question 33

A researcher hypothesizes that people of personality type K score higher than people of personality type R on an intelligence test. The S_Difference turned out to be .9, while the mean score of type K people was 18.8 and the mean score for type R people was 21.3. What is the t score?

A)t = (18.8-21.3)/ .9² = -3.09
B)t = (18.8-21.3)(.3)= 8.33
C)t = (18.8-21.3)/ .9 = -2.78
D)t = (18.8-21.3)/ [(2)(.9)] = -1.39

Question 34

What is the research hypothesis in this example?

A)The means of Population 1 and Population 2 are the same
B)The mean of Population 2 is greater than Population 1
C)The means of Population 1 and Population 2 are different
D)The mean of Population 1 is greater than the mean of Population 2

Question 35

For a study using a t test for independent means, the approximate number of participants needed for 80% power for an estimated small effect size and using a one-tailed test is:

A)50
B)64
C)310
D)393

Question 36

The effect size for the t test for independent means is the difference between the sample means divided by the:

A)pooled estimate of the population SD
B)SD of the distribution of differences between means
C)SD of difference scores
D)variance of difference scores for the population

Question 37

For a study using a t test for independent means, the approximate number of participants needed for 80% power for an estimated large effect size and using a two-tailed test is:

A)26
B)50
C)64
D)310

Question 38

For the following question(s): Suppose a researcher wants to study the effectiveness of a new reading program for students who have not acquired the necessary reading skills by the time they reach the eighth grade. A randomly selected group of 50 students from a local junior high with poor reading skills will undergo the new reading program. Another group of 50 randomly selected students with poor reading skills will undergo regular reading classes. A month later, the reading skills of all 100 students are assessed to determine whether the program was successful.
Which of the following is a population of interest in this study?

A)Population I: Students with poor reading skills who undergo the new reading program
B)Population II: The general population of readers
C)Population II: Students with poor reading skills who undergo regular reading classes
D)Both A and C are correct

Question 39

In an experiment involving 50 participants, which study would have the most power?

A)A study with 5 in the experimental group and 40 in the control group
B)A study with 40 in the experimental group and 10 in the control group
C)A study with 25 in the experimental group and 25 in the control group
D)All would have the same power because power depends on the total number of participants; how they are divided between groups makes no difference.

Question 40

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 20.
B)The populations are both negatively skewed.
C)The populations are both positively skewed.
D)The populations are dramatically skewed in opposite directions.

Question 41

"t = (Sample M-Population M)/ SM" is used to conduct a(n)__________.

Question 42

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

Question 43

In a study of the effects of a particular drug on creativity, 15 research participants took a creativity test twice: once in a normal mental state and once under the influence of the drug. In this study, you would use a t test for __________ to analyze the results.

Question 44

In a study of the effects of smell on concentration, 20 participants performed a standard task while exposed to an unpleasant smell and another 20 participants were tested on the same task but without being exposed to the unpleasant smell. You would use a t test for __________ to analyze results.

Question 45

Because Sample 1 is sometimes bigger (or smaller)than Sample 2, a(n)__________ is used to combine the two estimates of the population variance into an overall pooled estimate.

Question 46

The distribution of differences between means is essentially the same concept as the distribution of difference scores. (True or False)

Question 47

A study has 6 participants in the experimental group and 16 participants in the control group. What is the harmonic mean of these sample sizes?

A)6)3
B)8)7
C)9)2
D)10.01

Question 48

Degrees of freedom 1 + Degrees of freedom 2 = __________

Question 49

"S²_Pooled / N₁" is the formula to find the variance of the __________ for Population 1.

Question 50

"t = (M1-M2)/ S_Difference" is used to conduct a(n)__________.

Question 51

You take a mean from a population's distribution of means and subtract it from a mean from another population's distribution of means. You do this repeatedly many times. You would be making a(n)__________.

Question 52

Which of the following is an example of the most common way for a t test for independent means to be reported in a research article?

A)t(i:29)< .05
B)independent t(15): 30.16, p: significant
C)t(independent)= 2.93, p = .01
D)t(45)= 3.52, p < .05

Question 53

The __________ is used to compare scores from __________.

Question 54

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

Question 55

If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is __________.

Question 56

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

Question 57

A research article based on a t test for independent means reports a result as "t(28)= 4.21, p < .01."

A)The result was statistically significant.
B)There were 30 participants in the study.
C)The t score was 4.21.
D)All of the above.

Question 58

An important focus in the t test for independent means is the difference between the means of the two groups. (True or False)

Question 59

In a t test for independent means, the difference between the means of your two samples is divided by the standard deviation of the __________ to get the t score.

Question 60

A study has 18 participants in the experimental group and 7 participants in the control group. What is the harmonic mean of these sample sizes?

A)18/(18 + 7)+ 7/(18 + 7)= .6
B)(2)(18)/(18 + 7)+ (2)(7)/(18 + 7)= 2.0
C)(2)(18)(7)/(18 + 7)= 10.08
D)(18 + 7)2/(18 + 7)= 25

Question 61

For a t test for independent means, in order to determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected, one should consult the __________.

Question 62

In a certain study, an experimental group contains 45 participants while the control group contains 35 participants. What is the harmonic mean in this study?

Question 63

Results of a t test for independent means may be reported in a table where each significant difference is shown by __________.

Question 64

In an experiment with 48 participants, you are most likely to get a significant result if you assign __________ participants to the experimental group and __________ participants to the control group.

Question 65

"[(2)(N1)(N2)]/(N1 + N2)" is the formula for the __________.

Question 66

In a single-sample t test, suppose the mean of your sample 1 is 90, the mean of Population 2 is 75, and the standard deviation of the distribution of differences between means is 6. What is the t score?

Question 67

A manager of a small store wanted to discourage shoplifters by putting signs around the store saying "Shoplifting is a crime!" However, he wanted to make sure this would not result in customers buying less. To test this, he displayed the signs every other Wednesday for 8 weeks, for a total of 4 days displayed. He recorded the store's sales for those four Wednesdays and then recorded the store's sales for the four alternate Wednesdays, when the signs were not displayed. On the Wednesdays with the sign, the sales were 83, 73, 81, and 79. On the Wednesdays without the sign, sales were 84, 90, 82, and 84.
Do these results suggest that customers buy less when the signs are displayed? (Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Figure the effect size.
d. Explain what you did to a person who is familiar with the t test for a single sample but is unfamiliar with the t test for independent means.

Question 68

In a t test for independent means, an effect size of __________ is considered medium. (Provide a value.)

Question 69

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

Question 70

What is the harmonic mean in a study with two groups of participants in which Group 1 has 27 individuals and Group 2 has 35 individuals?

Question 71

Estimated effect size for the t test for independent means is determined using what formula?

Question 72

When sample sizes are unequal, the __________ tells you the equivalent size that two equal-sized samples would need to be for a study to have the same amount of power.

Question 73

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

Question 74

In a t test for independent means, an effect size of __________ is considered large. (Provide a value.)

Question 75

An assumption for a t test for independent means is that each of the population distributions follows a normal curve. (True or False)

Question 76

A study with two groups of 10 participants each, using a t test for independent means, resulted in a t of 2.21, which was significant at the .05 level. The standard way of describing this in a research article would be as follows: __________.

Question 77

t tests for independent means are usually reported in research articles with the means of the two groups plus the __________ , __________ , and __________.

Question 78

For each of the following studies, say whether you would use a t test for a single sample, t test for dependent means, or a t test for independent means.
(a)A psychology researcher randomly assigns a group of 50 high school students to receive a new assertiveness training program and 45 other high school students to receive the standard after-school program that focuses on social skills. She later measures how well each group performs on a measure of interpersonal assertiveness.
(b)A psychologist measures 100 patients in terms of their anxiety levels before and after undergoing a newly developed treatment.
(c)The coach of your college football team conducts an informal survey showing that members of the team study an average of 3.5 hours per day. The coach makes the claim that this is equivalent to the amount of time students at the college study in general. You feel that the coach is incorrect. You randomly select 50 students from the college and ask them how much they study each day. Your result is that these 50 students study an average of 5.2 hours per day.
(d)A researcher tests the memory scores of each of a group of 15 students twice, once while in a very noisy room and once while in a quiet room. She then compares the scores.
(e)A researcher measures the intelligence of college students (n = 25)who are first born in their families compared to those who were born last in their families (n = 40).

Question 79

Power is greatest in a t test for independent means when the sample sizes of the two groups are unequal. (True or False)

Question 80

A team of researchers studied the effects of sleep deprivation on decay of short-term memory. Eight participants stayed in a lab for 2 days. Four were randomly assigned not to sleep during that period. The other four were allowed to sleep when they wanted to do so. At the end of the 2 days, the participants completed a short-term memory task. Here are the results:
Mean Time (Seconds)for Remembering
Based on these results, does sleep deprivation reduce short-term memory? (Use the.05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Figure the effect size. What can you say from a power perspective?
d. Explain what you did to a person who is familiar with the t test for a single sample but is unfamiliar with the t test for independent means.