1- Why is it necessary to estimate the standard error when a t statistic is used?

2- Several different factors influence the value obtained for a t statistic. For each of the

following, describe how the value of t is affected. In each case, assume all other factors are held constant.

a- What happens to the value of t when the variability of the scores in the sample increases?

b- What happens to the value of t when the number of scores in the sample increases?

c- What happens to the value of t when the difference between the sample mean and the hypothesized population mean increases?

3- Why is a t-distribution generally more variable than a normal distribution?

4- Describe the general characteristics of a research study for which an independent measures t-test would be the appropriate test statistic.

5- What happens to the value of the independent measures t statistic as the difference between the two sample means increases? What happens to the t value as the variability of the scores in the two samples increases?

6- One sample has SS = 63 and a second sample has SS = 45.

a- Assuming that n = 10 for both samples, find each of the sample variances and

then calculate the pooled variance. What do you notice about the pooled

variance?

b- Now assume we have n = 10 for the first sample and n = 16 for the second

sample. Find each of the sample variances and then calculate the pooled variance. What do you notice about the pooled variance?

7- For each of the following, indicate the appropriate hypothesis test (one-sample z-test, one-sample t-test, independent-measures t-test, or dependent-measures t-test). If your response is dependent-measures t-test, indicate the "flavor" of the dependent measures t-test.

a- A study measuring differences in attitudes about morality among Democrats and Republicans

b- A study testing whether night-shift workers sleep the recommended 8 hours per day

c- dA researcher examines the effect of relaxation training on test anxiety. One sample of subjects receives relaxation training for three weeks. A second sample serves as a control group and does not receive the treatment. The researcher then measures anxiety levels for both groups in the test taking situation.

d- A different researcher also conducts a study involving relaxation training. Baseline levels of test anxiety are recorded for a sample of subjects. Then all subjects receive relaxation training for 3 weeks and their anxiety levels are

measured again. e. In a test anxiety study, two samples are used. Subjects are assigned to groups so

they are matched for self-esteem and grade-point average. One sample receives relaxation training for three weeks and the second serves as a no-treatment control group. Test anxiety is measured for both groups at the end of three weeks.

8- Explain the difference between a matched subjects design and a repeated measures design.

9- The values listed below are the obtained values for a t-statistic. What is your decision for each if df = 36 and = .05 for a two-tailed test.

a- tobt = 2.050

b- tobt = 1.680

c- tobt = 2.834

d- tobt = -3.030

10- State the critical value given the following:

a- One-sample t-test, two tailed test, = .05, n = 12

b- Z-test, two-tailed, = .01

c-Independent measures t-test, two-tailed, df in each group is n = 12, = .01

d- Dependent measures t-test, one-tail, = .05, nD = 17

11- While researching lifestyle changes to improve heart health, you come across a research article reporting that the average American consumes about 2700 calories per day ( = 2700). You come across another article that refutes this, stating that a sample of Americans consumed significantly less than this mean on average, t(50) = 2.993, p < .05, r2 = 0.15. Assuming this test was a one-sample t-test, answer the following questions:

a -Is this a significant effect?

b- What is the proportion of variance for this effect?

12. Find the number of subjects in the entire study based on the research design:

a- A researcher conducts an independent-measures study comparing two

treatments and report the t statistic as t(30) = 2.085. How many individuals

participated in the entire study?

b- A researcher conducts a one-sample study comparing a sample mean to the

population mean. If the researcher reports the t statistic as t(25) = 4.57. How

many individuals participated in the entire study?

c- A researcher performed a matched-subjects design and reports the t statistic as

t(23) = 4.53. How many individuals participated in the entire study?

the critical values given the following conditions:

d- A researcher conducts an dependent-measures study comparing two treatments and report the t statistic as t(36) = 1.89. How many individuals participated in the entire study?