1. Although you can compute a z-score for a single score (a sample of n = 1), it is impossible to compute a t statistic for a sample that has only one score. Explain why.

2. A sample is selected from a population with = 80. After a treatment is administered to the individuals, the sample mean is found to be M = 75 and the variance is s2 = 100.

a. If the sample has n = 4 scores, then calculate the estimated standard error and

determine whether the sample is sufficient to conclude that the treatment has a

significant effect? Use a two-tailed test with = .05.

b. If the sample has n = 25 scores, then calculate the estimated standard error and

determine whether the sample is sufficient to conclude that the treatment has a

significant effect? Use a two-tailed test with = .05.

c. Describe how increasing the size of the sample affects the standard error and the

likelihood of rejecting the null hypothesis.

3. A sample of n = 16 individuals is selected from a population with = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33.

a. If the sample variance is s2 = 16, then calculate the estimated standard error and

determine whether the sample is sufficient to conclude that the treatment has a

significant effect? Use a two-tailed test with = .05.

b. If the sample variance is s2 = 64, then calculate the estimated standard error and

determine whether the sample is sufficient to conclude that the treatment has a

significant effect? Use a two-tailed test with = .05.

c. Describe how increasing variance affects the standard error and the likelihood of

rejecting the null hypothesis.

4. A researcher is testing the effect of a new cold and flu medication on mental alertness. A sample of n = 9 college students is obtained, and each student is given the normal dose of the medicine. Thirty minutes later, each student's performance is measured on a video game that requires careful attention and quick decision making. The scores for the nine students are as follows: 6, 8, 10, 6, 7, 13, 5, 5, 3.

a. Assuming that scores for students in the regular population average = 10, are the

data sufficient to conclude that the medication has a significant effect on mental performance? Test at the .05 level of significance.

b. Compute r2, the percentage of variance explained by the treatment effect.

c. explain a sentence demonstrating how the outcome of the hypothesis test and the measure

of effect size would be presented in a research report.

5. A sample of n = 16 scores has a mean of M = 58 with SS = 960. Use the sample to construct the 90% confidence interval for .