4. Critical Thinking All other conditions being equal, does a z or t value with larger magnitude have a larger or smaller corresponding P-value?

Before you solve each problem below, first categorize it by answering the following question: Are we testing a single mean, a difference of means, a paired difference, a single proportion, or a difference of proportions? Assume underlying population distributions are mound-shaped and symmetric for problems with small samples that involve testing a mean or difference of means. Then provide the following information for Problems 5–18.

(a) What is the level of significance? State the null and alternate hypotheses.

(b) Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?

(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) to (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.

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 by a small amount and therefore produce a slightly more

“conservative” answer. Answers may vary due to rounding.