1. Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?

2. A sample of n = 16 scores has a mean of M = 56 and a standard deviation of s = 12.

a. Explain what is measured by the sample standard deviation.

b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.

3. Find the estimated standard error for the sample mean for each of the following samples.

a. n = 9 with SS = 1152

b. n = 16 with SS = 540

c. n = 25 with SS = 600

4. Explain why t distributions tend to be flatter and more spread out than the normal distribution.

5. Find the t values that form the boundaries of the critical region for a two-tailed test with = .05 for each of the following sample sizes:

a. n = 4

b. n = 15

c. n = 24

6. Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailed test with = .01 for each of the following sample sizes.

a. n = 10

b. n = 20

c. n = 30

7. The following sample of n = 4 scores was obtained from a population with unknown parameters. Scores: 2, 2, 6, 2

a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.) b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)

8. The following sample was obtained from a population with unknown parameters. Scores: 13, 7, 6, 12, 0, 4

a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.)

b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)

9. A random sample of n = 12 individuals is selected from a population with = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 with SS = 297.

a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.)

b. How much difference is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.)

c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with = .05.