Chapter 10
An independent-measures study uses two samples, each with n = 10, to compare two treatment conditions. What is the df value for the t statistic for this study?
18
Using an independent-measures t, the 90% confidence interval for the difference between two population means ranges from 19 to 23. Based on this confidence interval, you can conclude that the difference between the two sample means is _____.
21 points
Two samples, each with n = 5 scores, have a pooled variance of 40. What is the estimated standard error for the sample mean difference?
4
One sample has a variance of s2 = 10 and a second sample has a variance of s2 = 6. If the two samples have the same number of scores, what is the pooled variance for the two samples?
8
For an independent-measures research study, the data show an 8-point difference between the two treatment means and a pooled variance of 4. Given this information, what is the value of Cohen's d?
8/2
Which of the following accurately describes an independent-measures study?
It uses a different group of participants for each of the treatment conditions being compared.
One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can you conclude about the pooled variance for these two samples?
It will be closer to 30 than to 20.
Which of the following sets of data would produce the largest value for an independent-measures t statistic?
The two sample means are 10 and 20 with variances of 20 and 25.
In an independent-measures hypothesis test, what must be true if t = 0?
The two sample means must be equal.
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic?
The two samples both have n = 30 with sample variances of 20 and 25.
Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?
a large mean difference and small sample variances
An independent-measures study produces sample means of M1 = 35 and M2 = 31 and a pooled variance of 25. For this study, Cohen's d = ______.
d = 4/5
If n = 15 for each sample, which of the following sets of data provides the clearest difference between the two samples?
a sample mean difference of 10 points with s2 = 5 for both samples
A researcher conducts an independent-measures study examining how the brain chemical serotonin is related to aggression. One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin. A second sample of rats receives a drug that lowers brain levels of serotonin. Then the researcher tests the animals by recording the number of aggressive responses each of the rats display. The data are as follows. Control Low Serotonin n = 10 n = 15 M = 14 M = 19 SS = 180.5 SS = 130.0 a. Does the drug have a significant effect on aggression? Use an alpha level of .05, two tails. b. Compute Cohen's d to measure the size of the treatment effect.
a. H0: µ1 µ2 = 0 (no effect). With df = 23, the critical region consists of t values beyond ±2.069. For these data the pooled variance is 13.5, the standard error is 1.5, and the t statistic is t(23) = 3.33. Reject H0. Lower serotonin levels cause an increase in aggression. b. Cohen's d = 5/13.5 = 1.36.
One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, then what is the value of Cohen's d?
1.00
An independent-measures study comparing two treatment conditions produces a t statistic with df = 18. If the two samples are the same size, how many participants were in each of the samples?
10
Describe the data that are collected for an independent-measures t test and the hypotheses that the test evaluates.
An independent measures t statistic requires scores from two separate samples. The null hypothesis states that there is no difference between the means of the two populations (or treatments) from which the samples were obtained.
If the sample mean difference is 3 points, which of the following sets of data would produce the largest value for Cohen's d?
Cohen's d is the same for all three of the samples.
Two samples, each with n = 8, produce an independent-measures t statistic of t = -2.15. Which of the following decisions is justified?
Fail to reject H0 with α = .05 and fail to reject with α = .01.
An independent-measures research study uses two samples, each with n = 12 participants. If the data produce a t statistic of t = 2.08, then 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.
An independent-measures research study uses two samples, each with n = 12 participants. If the data produce a t statistic of t = 2.50, then 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.
The following data are from an independent-measures experiment comparing two treatment conditions. Treatment 1 Treatment 2 4 19 5 11 12 18 10 10 10 12 7 14 a. Do these data indicate a significant difference between the treatments at the .05 level of significance? b. Compute r2 to measure the size of the treatment effect. c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.
a. For treatment 1, M = 8 and SS = 50. For treatment 2, M = 14 and SS = 70. For these data the pooled variance is 12, the standard error is 2, and the t statistic is t(10) = 3.00. With α = .05 and df = 10, the critical boundaries are ±2.228. Reject H0. b. For these data, r2 = 9/19 = 0.474. c. The data indicate a significant difference between treatments, t(10) = 3.00, p < .05, r2 = 0.474.
An educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Frequent Quizzes Two Exams n=20 n = 20 M = 73 M = 68 a. If the first sample variance is s2 = 38 and the second sample has s2 = 42, do the data indicate that testing frequency has a significant effect on performance? Use a two-tailed test at the .05 level of significance. (Note: Because the two sample are the same size, the pooled variance is simply the average of the two sample variances.) b. If the first sample variance is s2 = 84 and the second sample has s2 = 96, do the data indicate that testing frequency has a significant effect? Again, use a two-tailed test with α = .05. c. Describe how the size of the variance affects the outcome of the hypothesis test?
a. The null hypothesis states that in the general population there is no mean difference between the two testing conditions. Pooled variance = 40, standard error = 2, t(38) = 2.50. With α = .05 and df = 30 (because 38 is not listed in the table), the critical boundaries are ±2.042. Reject the null hypothesis. b. The pooled variance is now 90, the standard error is 3, and t = 1.67. With df = 38, we fail to reject the null hypothesis. c. With larger variance, the 5-point mean difference is no longer significant. In general, larger variance lowers the likelihood of finding a significant difference.
For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples?
increase the likelihood of rejecting H0 and have little or no effect on measures of effect size
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 100
A researcher reports an independent-measures t statistic with df = 30. If the two samples are the same size (n1 = n2), then how many individuals are in each sample?
n=16
For an independent-measures research study, what is measured by Cohen's d or r2?
the size of the difference between the two treatments
The results of an independent-measures research study are reported as "t(20) = 2.12, p < .05, two tails." For this study, what t values formed the boundaries for the critical region?
±2.086
An independent-measures study with n = 6 in each sample, produces a sample mean difference of 4 points and a pooled variance of 12. What is the value for the t statistic?
2
The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 16. If there are n = 8 scores in each sample, then what is the estimated standard error for the sample mean difference?
2
An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments. What is the df value for the t statistic for this study?
23
A researcher reports t(22) = 5.30, p < .01 for an independent-measures experiment. How many individuals participated in the entire experiment?
24
What is the pooled variance for the following two samples?
24
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?
4/20
The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points. If there are n = 8 scores in each sample, then the value for the t statistic is _____.
6/2
Which of the following confidence intervals also indicates a significant difference between treatments with α = .05?
Estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence.
A major company would like to assess the impact of using a professional trainer to conduct a confidence-building workshop with their salespeople. A sample of 16 workers is obtained. Half (n = 8) attend the workshop and the other half (n = 8) serves as a control group. Two weeks later, each of the participants is given a questionnaire measuring the level of self-confidence. The data are as follows: Controls Workshop M = 17.5 M = 22.7 SS = 100 SS = 124 Use the sample data to construct an 80% confidence interval for the mean difference in confidence between the control group and the workshop conditions.
For these data the pooled variance is 16 and the estimated standard error is 2. With df = 14 and 80% confidence, use t = +-1.345. The confidence interval is m1 - m2 = 5.2 +-1.345(2) and extends from 2.51 to 7.89.
Two samples, each with n = 6 subjects, produce a pooled variance of 20. Based on this information, what is the estimated standard error for the sample mean difference?
the square root of (20/6 + 20/6)
For the independent-measures t statistic, what is the effect of increasing the sample variances?
decrease the likelihood of rejecting H0 and decrease measures of effect size
One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has s2 = 10. If the pooled variance is computed for these two samples, then the value obtained will be ______.
exactly half way between 6 and 10
For the independent-measures t statistic, what is the effect of increasing the difference between sample means?
increase the likelihood of rejecting H0 and increase measures of effect size
Assuming that there is a 5-point difference between the two sample means, which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?
large sample sizes and small sample variances
Which combination of factors is most likely to produce a significant value for an independent-measures t statistic?
large samples and small variance
One sample has n = 5 scores and the second has n = 10 scores. If the pooled variance for the two sample is 30, then what is the value of the estimated standard error for the sample mean difference?
the square root of (30/5 + 30/10)
Which of the following is the correct null hypothesis for an independent-measures t test?
μ1 - μ2 = 0