Chapter 9, Problem 8CR

Before you solve each problem below, first categorize it by answering the following question: Are we testing a single mean or a single proportion? Assume underlying population distributions are mound-shaped and symmetric for problems with small samples that involve testing a mean. Then provide the following information for Problems 7-14.

(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? Compute the sample test statistic and corresponding distribution 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) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$?

(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.

Matches: Number per Box The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box. with $\sigma =9$. A random sample of 94 Nero matchboxes shows the average number of matches per box to be 43.1. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?