Deck 14: Hypothesis Tests Applied to Means: Two Independent Samples

Question 1

In the previous example, how many df do we have?

A) 25
B) 43
C) 41
D) 21.5

Answer 1

41

Question 2

Which of the following would make you believe that you have two independent groups?

A) Subjects were assigned to groups at random as they arrived for testing.
B) There are 25 subjects in Group 1 and 45 subjects in Group 2.
C) Every subject supplies one score.
D) All of the above.

Answer 2

All of the above.

Question 3

When we speak about pooling variances we are referring to

A) averaging the two groups' variances.
B) using the variance of the larger group.
C) adding up the variances in each of two groups and dividing by 2.
D) taking the variance of both sets of data combined.

Answer 3

averaging the two groups' variances.

Question 4

The most important characteristic of two independent samples is

A) we measure the same subjects on two separate times.
B) the subjects in one sample are part of the same family as subjects in the other sample.
C) the set of scores for one sample is uncorrelated with the scores in the other sample.
D) the subjects in a group are people who know each other.

Question 5

When testing the means of independent samples, the null hypothesis is best thought of as

A) the mean of population 1 is equal to the mean of population 2.
B) the mean of population 1 is unequal to the mean of population 2.
C) the mean of a set of difference scores is equal to 0.
D) the two population means don't differ by more than 10 points.

Question 6

Given the following equation, the only difference between this and our original equation for z is:

A) the original z required a normal distribution.
B) we have substituted information about differences in place of information about observations.
C) the equations are of the same general form.
D) both b) and c).

Question 7

Which of the following would most likely NOT be independent samples?

A) Group 1 contains wives and Group 2 contains their husbands.
B) Group 1 contains women and Group 2 contains men.
C) Group 1 contains dyslexic children and Group 2 contains non-dyslexic children.
D) Group 1 contains smokers and Group 2 contains nonsmokers.

Question 8

The variance sum law deals with

A) the variance of the sum of two or more variables.
B) the variance of the difference of two or more variables.
C) the variance of any single variable.
D) both a) and b).

Question 9

In the anorexia example comparing Family Therapy and Control conditions the null hypothesis would be

A) m _FT = m _C
B) m _FT ≠ m _C
C) m _FT m _C
D) m _FT > m _C

Question 10

When we have an independent sample t test, the degrees of freedom are equal to

A) N
B) N ₁ + N ₂ - 1
C) N ₁ + N ₂ - 2
D) N - 1

Question 11

When variables A and B are independent, the variance of A - B is equal to

A) the variance of A plus the variance of B.
B) the variance of A.
C) variance of A minus the variance of B.
D) it cannot be determined from the information given here.

Question 12

We would NOT pool the variances if

A) we had too few subjects.
B) we had too many subjects.
C) The means were clearly different.
D) we had very unequal sample variances.

Question 13

The distribution of differences between means is

A) normally distributed for very large samples.
B) approaches normal as sample sizes increase.
C) may be nonnormal for small samples.
D) all of the above.

Question 14

The t statistic differs from z in that

A) it applies to variances.
B) it is used when population variances are not known.
C) it involves an assumption of normality.
D) and b) but not c).

Question 15

To go from the equation in the previous problem to the equation for t we must

A) substitute sample means for population means.
B) substitute sample variances for population variances.
C) substitute sample standard deviations for population variances.
D) draw very large samples.

Question 16

The following data are taken from Chapter 14 and refer to a study of weight gain in treated and untreated girls suffering from anorexia.

Which of the following formula for t in this situation would be a correct one?

A)
B)
C)
D)

Question 17

Our assumption that population variances are equal is called the assumption of

A) equal dispersion.
B) heterogeneity of variance.
C) homogeneity of variance.
D) pooled variances.

Question 18

A weighted average is

A) the average of two weights.
B) an average that gives greater influence to the larger sample.
C) an average that reduces the influence of the larger sample.
D) the balance between the sample size and the mean.

Question 19

Which of the following formulae for t is correct?

A)
B)
C)
D) all of the above

Question 20

The reason that we pool variances is to

A) inflate our error term.
B) get a better estimate of error variance.
C) reduce the sample variance.
D) increase the size of t .

Question 21

When we say that two independent variables, such as gender and age, are confounded, we mean that

A) one variable blocks the influence of the other.
B) we cannot completely tell the effect of gender apart from the effect of age.
C) we cannot do anything with the study.
D) the data were collected carelessly.

Question 22

A researcher was interested in examining the different levels of aggression shown by college students and prisoners with life sentences. Aggression was measured by surveys given during one session. Which analysis should the researcher perform on the mean aggression scores of the groups?

A) related means t test
B) independent means t test
C) correlation
D) regression

Question 23

Using the conservative test in which variances were not pooled that was described in the text, on how many degrees of freedom would the t test on groups of 65 and 21 participants be based?

A) 65 - 1 = 64 df
B) 21 - 1 = 20 df
C) 65 + 21 - 2 = 84 df
D) (65 + 21) ÷ 2 = 43 df

Question 24

An important reason for using random assignment in a study with independent groups is to

A) prevent any systematic differences between groups on extraneous variables.
B) be able to generalize to broader populations.
C) rule out competing interpretations of any differences we find.
D) a and c

Question 25

Mean scores in Tetris were recorded for both math majors and English majors. The mean score for math majors was 20,752 (s₁² = 851, N₁ = 17) and the mean score for English majors was 14,922 (s₂² = 395, N₂ = 56). The pooled variance would probably be closest to which value?

A) 800
B) 623
C) 500
D) 900

Question 26

One of our best aids in handling problems of non-normality is

A) the variance sum law.
B) the central limit theorem.
C) the non-normality correction.
D) the Stroop test.

Question 27

Which of the following is a reason why we may NOT find a significant difference between two groups?

A) The sample size was too small.
B) The true mean difference between the groups was too small.
C) The variability between the groups was too large.
D) all of the above

Question 28

In which of the following cases is it most useful to pool the variances?

A) s₁² = 7.3, N₁ = 15 and s₂² = 8.1, N₂ = 15
B) s₁² = 7.3, N₁ = 15 and s₂² = 52.3, N₂ = 6
C) s₁² = 8.4, N₁ = 13 and s₂² = 12.1, N₂ = 19
D) none of the above

Question 29

In the previous test on the treatment of anorexia, the resulting t was -3.22, which was significant (p

A) the family therapy condition had a mean that was reliably less than the mean of the control condition.
B) the family therapy condition had a mean that was reliably more than the mean of the control condition.
C) the family therapy condition had a mean that was unreliably less than the mean of the control condition.
D) the family therapy condition had a mean that was unreliably more than the mean of the control condition.

Question 30

In the example in the text assessing the effect of family therapy on anorexic girls by the mean levels of weight gain, the difference between the independent samples design used there and the related means design used in Chapter 13 is that the independent samples design

A) compared the mean weight gained by anorexic girls in family therapy to the mean weight gained by girls in a control group.
B) compared the means of pre-therapy weights to the means of post-therapy weights.
C) assumed the weight gains of the two groups would be related.
D) assessed family therapy as a predictor of weight gain.

Question 31

The null hypothesis of an independent samples t test is

A) r = 0.
B) m ₁ > m ₂.
C) m ₁ = m ₂.
D) m ₁ ≠ m ₂.

Question 32

If we built on Doob and Gross's study of horn-honking behavior to compare the time it takes for people to honk at an older car versus the time to honk at an expensive newer car, we could set it up as

A) an independent sample design.
B) a repeated measures design.
C) neither a nor b
D) It could be designed either way, depending upon our needs.

Question 33

When we have very unequal sample variances, we should

A) check our work very carefully when we pool the variances.
B) not pool the variances.
C) average the variances, but not weight them with the degrees of freedom.
D) run some different analysis.

Question 34

If we reject the null hypothesis with a two-tailed test in the previous anorexia condition, we would side with which of the following alternatives?

A) m _FT = m _C
B) m _FT ≠ m _C
C) m _FT m _C
D) m _FT > m _C

Question 35

In deciding whether or not to pool the variances in calculating a t score, one should consider

A) the differences in the sample variances.
B) the differences in the sample sizes.
C) both a and b
D) neither a nor b

Question 36

For a very conservative test when we don't pool the variances we should

A) work at a = .01 instead of a = .05.
B) insist that the critical value of t be twice the tabled value.
C) use a much reduced number of degrees of freedom.
D) throw up our hands and call the problem too difficult.

Question 37

What is the null hypothesis of the above example?

A) Prisoners are more aggressive than college students.
B) College students are more aggressive than prisoners.
C) There is no relationship between stress levels and groups.
D) Prisoners and college students are not different in aggression levels.

Question 38

The statistical test that compares two or more means is a(n)

A) t-test.
B) z -score.
C) ANOVA.
D) correlation.

Question 39

What statistical test is used for two independent groups?

A) z -score
B) chi-square
C) between-subject t-test
D) ANOVA

Question 40

The normality assumptions behind the independent groups t test

A) is one that we cannot get around.
B) diminishes in importance as the variance of the two groups increases.
C) is absolutely unimportant.
D) diminishes in importance as the sample sizes increase.

Question 41

Explain an appropriate method to compare means from independent samples when the sample variances are heterogeneous.

Question 42

In an independent samples t-test comparing the means of a sample of 25 and a sample of 30, the df = 53.

Question 43

Children reared in orphanages and children reared by their biological parents are two independent groups.

Question 44

Normality of distributions is an assumption involved in the use of a t-test.

Question 45

What is the two-tail critical value for an independent samples t-test (assuming heterogeneity of variance) given the following samples sizes and p = .05?
a. N₁ = 10; N₂ = 10
b. N₁ = 15; N₂ = 10
c. N₁ = 27; N₂ = 25

Question 46

p(10 ≤ (µ₁ -  µ ₂) ≤  15) = .95, means that there is a 95% chance that the samples were drawn from populations that have means between 10 and 15.

Question 47

Pooled variance is the sum of the variance from two samples.

Question 48

Indicate whether or not it would be appropriate to use pooled variances to calculate t given the following information. Explain your answers.
a. s₁² = 1.5, N₁ = 30 and s₂² = 8.5, N₂ = 50
b. s₁² = 10, N₁ = 40 and s₂² = 15, N₂ = 48

Question 49

Sample variances are always pooled when computing independent samples t-tests.

Question 50

A group of children exposed to violence on television (N = 20) scored higher on a measure of aggression than a group of children who were not exposed to violence on television (N = 22). t = 1.25. What can you conclude?

Question 51

A chess team advisor wanted to examine how long it took his top two players, Fishy Bobber and Chet Mate, to complete their moves. Over the course of 50 matches each, Fishy averaged 330 seconds to move while Chet averaged 420 seconds to move. If the overall standard deviation for Fishy and Chet was 45 seconds, what was the effect size of their difference?

A) 1.0
B) 90
C) 2.0
D) Not enough information is given.

Question 52

A researcher thinks that people who drive red cars drive faster than people who drive white cars. He recorded the speed of a random sample of red and white cars on a highway. The data follow.

a. What is the research hypothesis?
b. Is a one-tail or a two-tail test more appropriate?
c. Calculate t.
d. Is the research hypothesis supported? Explain?

Question 53

Calculate the pooled variance given the following information.
a. s₁² = 26, N₁ = 30 and s₂² = 32, N₂ = 40
b. s₁² = 3.5, N₁ = 12 and s₂² = 4.6, N₂ = 18

Question 54

A political analyst wants to know if there are differences in how men and women are perceiving his candidate. In his sample, political party membership does not differ for males and females. Thus, gender and political party are confounded.

Question 55

We want to compare the scores of two different groups of people, those who are high in authoritarianism versus those who are low in authoritarianism, on a scale that measures leadership ability. What is the best statistical test to perform to see if the two groups are different from each other on this measure?

A) paired samples t-test
B) t-test for independent groups
C) factorial ANOVA
D) one way ANOVA

Question 56

According to the variance sum law, the variance of the difference of two independent variables is equal to the difference of their variances.

Question 57

Using the data from the previous example, what is the 95% confidence interval for the true difference in speed?

Question 58

Homogeneity of variance means that two samples were drawn from populations with equal variances.

Question 59

The measure of the effect size for the difference between two groups is best seen as

A) the difference in their means.
B) .
C) the ratio of the means.
D) all of the above

Question 60

When the assumption of homogeneity of variance is violated, the two sample means cannot be compared with a t-test.

Question 61

Given the following data, calculate and interpret t .

Question 62

Refer to the following output to answer these questions.

a. Has the assumption of homogeneity of variance been met?
b. Which t-test should be used to interpret the data?
c. Write a sentence summarizing the results of the t-test.

Question 63

A movie critic believes people linger in the theatre after a movie for longer periods following dramas than comedies. The data follow.

a. What is the research hypothesis?
b. Is a one-tail or a two-tail test more appropriate?
c. Calculate t .
d. Is the research hypothesis supported? Explain