Chapter 10 The t Test for Two Independent Samples

One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is s2p = 16, what is the value of Cohen's d?

d = 1.00

A research study has two samples, each with n = 6, and the two experimental treatments used in each sample are being compared using an independent-measures t statistic. What is the df value for the t statistic in this study?

df = 10

An independent-measures research study uses n = 15 participants in one group and n = 12 participants in a second group to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?

df = 25

An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?

df = 38

Which of the following elements is always presented last in a statistical report statement describing the results of an independent-measures t test?

effect size

Which of the following confidence intervals indicates a significant difference between treatments with α = .05?

estimate that µ1 - µ2 is in an interval between 2 and 10 with 95% confidence

One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has a variance of s2 = 10. If the pooled variance is computed for these two samples, then the value obtained for the variance will be _____.

exactly halfway between 6 and 10.

For the independent-measures t statistic, what is the effect of increasing the sample variances?

a decrease in the likelihood of rejecting H0 and a decrease in measures of effect size

Which set of sample characteristics is most likely to produce a statistically significant value for the independent-measures t statistic and a large effect size when conducting a hypothesis test?

a large sample mean difference and small sample variances

Which of the following sets of data is most likely to produce a statistically significant mean difference when conducting an independent samples t test?

a sample mean difference of 10 points with n = 10 for each sample

For the independent-measures t statistic, what is the effect of increasing the difference between sample means?

an increase in the likelihood of rejecting H0 and an increase in measures of effect size

For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples?

an increase in the likelihood of rejecting H0 and little or no influence on measures of effect size

Which combination of factors is most likely to produce a statistically significant value for an independent-measures t statistic?

large sample sizes and small sample variances

A researcher predicts that scores in treatment A will be higher than scores in treatment B. Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?

mA < or equal to mB

Which of the following sets of data would produce the largest value for Cohen's d?

n = 10 for both samples, a pooled variance of s2p = 16, and a mean difference of 4 points

A researcher reports an independent-measures t statistic with df = 16. How many participants were in the entire study?

n = 18

A researcher reports t(22) = 5.30, p < .01, two tails for an independent-measures experiment. How many individuals participated in the entire experiment?

n = 24

Two separate samples are being used to estimate the population mean difference between two treatment conditions. Which of the following would produce the widest confidence interval?

n1 = n2 = 10 with a pooled variance of s2p = 100

Two samples, each with n = 9 scores, produce an independent-measures t statistic of t = +2.00. If the effect size is measured using r2, what is the value of r2?

r2 = 0.20

One sample has n = 18 with SS = 102 and M = 12. A second sample has n = 5 with SS = 171 and M = 8. Which of the following is the 95% confidence interval for the mean difference in confidence between the two samples?

4 ± 3.7856

Which of the following is true regarding assumptions underlying the independent-measures t formula for hypothesis testing.

As the discrepancy in sample sizes increases, the assumption that the two populations from which the samples are selected must have equal variances becomes more important.

Which of the following sets of data would produce the largest value for an independent-measures t statistic, assuming the difference between sample means is held constant?

The two samples both have n = 30, with sample variances of s2 = 20 and s2 = 25.

Which of the following is not an assumption underlying the independent-measures t formula for hypothesis testing.

The two samples must have equal sample sizes.

A researcher conducts a research study to examine whether there is a difference between two treatments regarding depression. Which of the following is consistent conceptually with the alternative hypothesis?

There is a difference between the two treatments among the general population regarding depression.

An independent-measures research study uses two samples, each with n = 15 participants. If the data produce a t statistic of t = 2.660, which of the following is the correct decision for a two-tailed hypothesis test?

reject the null hypothesis with α = .05 but fail to reject with α = .01

Two samples, each with n = 5 scores, have a pooled variance of s2p = 40. What is the estimated standard error for the sample mean difference?

s(M1 - M2) = 4

One sample has a sample size of n = 8 and SS = 168. A second sample has a sample size of n = 6 and SS = 126. What is the pooled variance for these two samples?

s2p = 24.50

An independent-measures study produces sample means of M1 = 20 and M2 = 17. If both samples have n = 18 and Cohen's d = 0.50, what is the value for the pooled variance?

s2p = 36

One sample has a variance of s2 = 10 and a second sample has a variance of s2 = 6. Which of the following most accurately describes the pooled variance for the two samples?

somewhere between 6 and 10

An independent-measures study with n = 5 in each sample produces a sample mean difference of 4 points and a pooled variance of 40. What is the value for the t statistic?

t = +1

A researcher is examining whether daily exercise influences mood. The researcher assigns n = 12 individuals to exercise for three months and finds an average mood score of M = 22 with SS = 182 after three months for individuals in this group. A second group of n = 7 individuals assigned to a control group for the three months has a mood score of M = 19 with SS = 90. Which of the following is most consistent with the results of conducting a two-tailed independent-measures t test with α = .05?

t = +1.58 and fail to reject the null hypothesis

What is the average value expected for the independent-measures t statistic if the null hypothesis is true?

t = 0

The narrower the confidence interval, the more precise it is. Which combination of factors will produce the most precise estimate of the difference between two population means?

two samples of n = 50 and 80% confidence

Which of the following is the correct null hypothesis for an independent-measures t test?

µ1 - µ2 = 0

Which of the following is the correct alternative hypothesis for an independent-measures t test?

µ1 - µ2 ≠ 0