Question 1

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.

Accepted Answer

Confounding occurs when the effects of two independent variables on the dependent variable cannot be distinguished from each other. In other words, it is not possible to completely isolate the effect of one independent variable from the other. This can create problems in interpreting the results of a study and making causal inferences.

Question 2

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

Accepted Answer

The researcher should perform an independent means t test to compare the mean aggression scores between the two groups. This is because the two groups are independent of each other (college students and prisoners with life sentences) and the researcher wants to compare their mean aggression scores. A related means t test would be appropriate if the researcher was comparing the aggression scores of the same group of individuals under different conditions (before and after an intervention, for example). Correlation and regression analyses would be appropriate if the researcher was examining the relationship between aggression and other variables, but they do not address the question of differences between groups.

Question 3

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

Accepted Answer

When using the conservative test where variances are not pooled, the degrees of freedom for the t-test are based on the smaller of the two groups. For a group of 21 participants, the degrees of freedom would be 21 - 1 = 20 df.

Question 4

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

Accepted Answer

Random assignment helps to ensure that any systematic differences between groups on extraneous variables are not driving the results, and it also helps to rule out competing interpretations of any differences we find. Random assignment does not necessarily help with generalizability to broader populations.

Question 5

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

Accepted Answer

The answer of Mean scores in Tetris were recorded for...

Question 6

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.

Accepted Answer

The central limit theorem is a powerful aid in handling problems of non-normality. It states that as the sample size increases, the distribution of the sample means will approach a normal distribution regardless of the shape of the underlying population distribution. This allows us to use normal distribution-based techniques even when the population distribution is non-normal.

Question 7

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

Accepted Answer

All of the listed options are reasons why a significant difference between two groups may not be found. A small sample size can lead to insufficient statistical power to detect a difference. A small true mean difference means the actual difference between the groups is minimal, making it harder to detect statistically. Large variability within the groups increases the overlap between the groups, making it harder to find significant differences.

Question 8

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

Accepted Answer

The answer of In which of the following cases is...

Question 9

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.

Accepted Answer

A negative t-value (-3.22) indicates that the mean of the experimental group (family therapy condition) was lower than the mean of the control group. However, because the result was significant (p < .05), it means that this difference was not due to chance. Therefore, the correct interpretation is that the family therapy condition had a mean that was reliably more than the mean of the control condition, as the significance indicates a reliable difference in the opposite direction of the negative value.

Question 10

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.

Accepted Answer

The independent samples design used in the example compared the mean weight gained by anorexic girls in family therapy to the mean weight gained by girls in a control group, while the related means design used in Chapter 13 compares the means of pre-therapy weights to the means of post-therapy weights. The independent samples design assumes that the two groups are independent and not related, while the related means design assumes that the weight gains of the two groups are related. The independent samples design did not assess family therapy as a predictor of weight gain, but rather assessed the effect of family therapy on weight gain by comparing it to a control group.

Question 11

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.

Accepted Answer

The null hypothesis of an independent samples t test assumes that the population means of the two groups being compared are equal, which is represented by the equation m ₁ = m ₂. Therefore, choice C is the correct answer.

Question 12

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.

Accepted Answer

This study could be designed as either an independent sample design (comparing two separate groups of drivers, one behind older cars and one behind newer cars) or a repeated measures design (the same drivers responding to both older and newer cars at different times), depending on the specific research questions and logistical considerations.

Question 13

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.

Accepted Answer

When we have very unequal sample variances, we should not pool the variances because the assumption of essentially equal variances for each treatment group may not hold, and pooling the variances can lead to inaccurate results. Instead, we should use a method that accounts for unequal variances, such as the Welch's t-test or a non-parametric test.

Question 14

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

Accepted Answer

Rejecting the null hypothesis with a two-tailed test means that we have evidence to support that there is a significant difference between the means of the two groups being compared. The symbol "≠" in option B indicates that the means are not equal, making it the best choice to side with if the null hypothesis is rejected. The other options either assume equality or do not provide enough information about the direction of the difference.

Question 15

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

Accepted Answer

Both the differences in sample variances and sample sizes should be considered when deciding whether or not to pool variances. If the sample sizes are relatively equal and the sample variances are not significantly different, then pooling the variances is appropriate. However, if the sample sizes are significantly different or the sample variances are significantly different, it may be more appropriate to use separate variances in the calculation of the t score.

Question 16

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.

Accepted Answer

When variances are not pooled, the degrees of freedom are reduced using the Welch-Satterthwaite equation, leading to a more conservative test.

Question 17

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.

Accepted Answer

The null hypothesis is the statement that there is no difference or no relationship between the variables being studied. In this case, the null hypothesis is that there is no difference in aggression levels between prisoners and college students. Therefore, choice D is the correct option.

Question 18

The statistical test that compares two or more means is a(n)
A) t-test.
B) z -score.
C) ANOVA.
D) correlation.

Accepted Answer

ANOVA (Analysis of Variance) is a statistical test used to compare two or more means, while t-test is used to compare the means of two groups. Z-score is a measure of standard deviations from the mean, and correlation is used to examine the relationship between two variables. Therefore, ANOVA is the best choice for comparing multiple means.

Question 19

What statistical test is used for two independent groups?
A) z -score
B) chi-square
C) between-subject t-test
D) ANOVA

Accepted Answer

The between-subject t-test is the appropriate statistical test for comparing the means of two independent groups. The other options (z-score, chi-square, ANOVA) are either used for different types of data or for comparing more than two groups.

Question 20

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.

Accepted Answer

As sample sizes increase, the distribution of sample means tends to become more normal due to the Central Limit Theorem. Therefore, the normality assumption becomes less important with larger sample sizes.

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

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

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?

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?

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

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?

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

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

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

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

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

The null hypothesis of an independent samples t test is

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

When we have very unequal sample variances, we should

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?

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

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

What is the null hypothesis of the above example?

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

What statistical test is used for two independent groups?

The normality assumptions behind the independent groups t test