1. Which of the following terms is not required when using the t statistic?
Hint: Think about the steps necessary to calculate a t-statistic from a set of scores.
A) n
B) σ
C) s or s2 or SS
D) df
2. What is measured by the estimated standard error, sM?
A) How much difference is reasonable to expect between a sample mean and the population mean.
B) How spread out the scores are in the population.
C) How much difference is reasonable to expect between the t statistic and the corresponding z-score.
D) How spread out the scores are in the sample.
3. A sample is selected from a population with μ = 80. If the sample has a mean of M = 85, which of the following will produce the largest value for t?
A) n = 25 and s2 = 4
B) n = 9 and s2 = 16
C) n = 25 and s2 = 16
D) n = 9 and s2 = 4
4. When n is small (less than 30), the t distribution is the following.
A) cannot be specified, making hypothesis tests impossible
B) is taller and narrower than the normal z distribution
C) is almost identical in shape to the normal z distribution
D) is flatter and more spread out than the normal z distribution
5. With α = .01, what are the boundaries for two-tailed critical region with a sample of n = 20 subjects?
A) t = ± 2.861
B) t = ± 2.845
C) t = ± 2.528
D) t = ± 2.539
6. With α = .05 and df = 8, the critical value for a one-tailed t test is t = 1.860. Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical value of t?
A) stay the same
B) decrease
C) not enough information to answer
D) increase
7. A sample of n = 25 scores produces a t statistic of t = -2.05. If the researcher is using a two-tailed test, what would be the correct statistical decision?
A) none of the other responses are correct.
B) The researcher can reject the null hypothesis with α = .05 but not with α = .01.
C) The researcher can reject the null hypothesis with either α = .05 or α = .01.
D) The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.
8. In a hypothesis test using a t statistic, what is the influence of a large sample variance?
A) The size of the variance has no impact on the outcome of the hypothesis test.
B) Larger variance tends to increase the likelihood of rejecting the null hypothesis.
C) Larger variance tends to lower the likelihood of rejecting the null hypothesis.
D) Cannot determine without more information.
9. Compared to a z-score, a hypothesis test with a t statistic requires less information about the population.
A) True
B) False
10. The shape of the t distribution changes as the sample size changes.
A) True
B) False
11. For a one-tailed test with α = .05 and a sample of n = 25, the critical value for the t statistic is t = 1.711.
A) True
B) False
12. A sample of freshmen takes a reading comprehension test and their scores are summarized below. If the mean for the general population on this test is μ = 12, can you conclude that this sample is significantly different from the population. Test with α = .05.
Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10.
A) No, this sample is not significantly different from the population.
B) Yes, this sample is significantly different from the population.
13. The results of an independent-measures study produce a t statistic with df = 36. How many individual participated in the entire study?
A) 73
B) 38
C) 74
D) 37
14. One sample has a variance of s2 = 20 and a second sample has a variance of s2 = 30. What is the most that can be said about the pooled sample variance for these two samples?
A) It is exactly equal to 25.
B) It is smaller than 20.
C) It is larger than 30.
D) It is somewhere between 20 and 30.
15. One sample of n = 5 scores has SS = 36. A second sample of n = 7 scores has SS = 64. What is the value of the pooled variance for these two samples?
Hint: Pay close attention to the order of operations for this calculation.
A) 36/5 + 64/7
B) 100/10
C) 100/12
D) 36/4 + 64/6
16. Which of the following sets of sample data would produce the largest value for an independent-measures t statistic. Assume that n = 10 for all samples. Note: You should not need to do any serious calculations to answer this question.
A) First sample: M = 30 and SS = 10, Second Sample: M = 50 and SS = 10
B) First sample: M = 30 and SS = 10, Second Sample: M = 35 and SS = 10
C) First sample: M = 30 and SS = 50, Second Sample: M = 50 and SS = 50
D) First sample: M = 30 and SS = 50, Second Sample: M = 35 and SS = 50
17. What is the estimated standard error for the independent-measures t statistic for the following two samples? Sample 1: n = 4 with SS = 100. Sample 2: n = 8 with SS = 140.
A) 24
B) 9
C) 242
D) 3
18. The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 12. If there are n = 6 scores in each sample, then the estimated standard error for the mean difference is the following.
A) 12
B) 2
C) 120
D) 4
19. The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 12. If there are n = 6 scores in each sample, then the value for the t statistic is the following.
A) 1
B) 4
C) 6
D) 2
20. An independent-measures research study uses two samples, each with n = 8 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?
A) cannot answer without additional information
B) Fail to reject the null hypothesis with either α = .05 or α = .01.
C) Reject the null hypothesis with α = .05 but fail to reject with α = .01.
D) Reject the null hypothesis with either α = .05 or α = .01.
21. Two samples, each with n = 15 individuals, are used to evaluate the difference between two treatment conditions. If the researcher uses a two-tailed test with α = .05, then the critical region for the t statistic begins at the following values.
A) t = ±2.045
B) t = ±2.048
C) t = ±2.145
D) t = ±2.131
22. For the independent-measures t statistic, increasing the sample mean difference will the chances of a significant t statistic and measures of effect size.
23. For a hypothesis test with an independent-measures t, the larger the two sample variances are, the greater the likelihood that you will reject the null hypothesis.
A) True
B) False
24. Pooled variance can always be obtained by adding two SS values and dividing by 2.
A) True
B) False
25. For an independent-measures study with M1 = 20, M2 = 16, and a pooled variance of 25, the estimated value for Cohen's d = 4/25.
A) True
B) False