1. A sample is selected from a population with μ = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s² = 64.
a. If the sample has n = 4 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen’s d to measure the size of the treatment effect. Use a two-tailed test with α = .05.
b. If the sample has n = 16 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate Cohen’s d to measure the size of the treatment effect. Use a two-tailed test with α = .05.
c. Describe how increasing the size of the sample affects the likelihood of rejecting the null hypothesis and the measure of effect size.

2. A sample of n = 16 indivduals is selected from a population with μ = 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 conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r² to measure the size of the treatment effect. Use a two-tailed test with α = .05.
b. If the sample variance is s² = 64, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r² to measure the size of the treatment effect. Use a two-tailed test with α = .05.
c. Describe how increasing variance affects the likelihood of rejecting the null hypothesis and the measure of effect size.

3. 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 μ.

4. A sample of n = 9 participants is obtained from a population with μ = 29, and a treatment is administered to the individuals in the sample. After treatment, the scores for the nine participants are as follows: 23, 33, 26, 28, 30, 26, 27, 25, 25.
a. Are the data sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.
b. Are the data sufficient to conclude that the treatment significantly decreased scores? Use a one-tailed test with α = .05.

5. 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.

1. A sample is selected from a population with μ = 50. After a trea...