Chapter 9.3, Problem 14P

For Problems 7-21, please provide the following information.

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

(b) Check Requirements What sampling distribution will you use? Do you think the sample size is sufficiently large? Explain. Compute the value of the sample test statistic and corresponding z value.

(c) Find the P-value of the lest statistic. 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.

Fishing: Northern Pike Athabasca Fishing Lodge is located on Lake Athabasca in northern Canada. In one of its recent brochures, the lodge advertises that $75\%$ of its guests catch northern pike over 20 pounds. Suppose that last summer 64 out of a random sample of 83 guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from $75\%$ (either higher or lower)? Use $\alpha =0.05$.