Basic Computation: Paired Differences Test For a random sample of 20 data pairs, the sample mean of the differences was 2. The sample standard deviation of the differences was 5. Assume that the distribution of the differences is mound-shaped and symmetric.

At the 1% level of significance, test the claim that the population mean of the differences is positive.

(a) Check Requirements Is it appropriate to use a Student’s t distribution for the sample test statistic?

Explain. What degrees of freedom are used?

(b) State the hypotheses.

(c) Compute the sample test statistic and corresponding t value.

(d) Estimate the P-value of the sample test statistic.

(e) Do we reject or fail to reject the null hypothesis?

Explain.

(f) Interpretation What do your results tell you?

For Problems 12–25 assume that the distribution of differences d is mound-shaped and symmetric.

Please provide the following information for Problems 12–25.

(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

(b) Check Requirements What sampling distribution will you use? What assumptions are you making?

Compute the value of the sample test statistic and corresponding t value.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts

(a) through (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?

(e) Interpret your conclusion in the context of the application.

In these problems, assume that the distribution of differences is approximately normal.

Note: For degrees of freedom d.f. not in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and therefore produce a slightly more

“conservative” answer.

AppendixLO1