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 a = 0.05.

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

(b) 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 test 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 a?

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