Chapter 8.2, Problem 14P

Please provide the following information for Problems 11–22.

1. (a) What is the level of significance? State the null and alternate hypotheses.
2. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic.
3. (c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
4. (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 α?
5. (e) Interpret your conclusion in the context of the application.

Note: For degrees of freedom d.f. not given 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.

14. Fishing: Trout Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is μ = 19 inches. However, the Creel Survey (published by the Pyramid Lake Paiute Tribe Fisheries Association) reported that of a random sample of 51 fish caught, the mean length was $\bar{x}=\text{18}.\text{5}$ inches, with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use α = 0.05.