Hosmer Lake, Oregon, has an Atlantic salmon catch-and-release program that has been very successful. The average fisherman€™s catch has been μ = 8.8 Atlantic salmon per day. Suppose that a new quota system restricting the number of fishermen has been put into effect this season. A random sample of fishermen gave the following catches per day:

i. Use a calculator with sample mean and sample standard deviation keys to verify that = 7.36 and s ‰ˆ 4.03.
ii. Assuming the catch per day has an approximately normal distribution, use a 5% level of significance to test the claim that the population average catch per day is now different from 8.8.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute 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)€“(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
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 €œconservative€ answer.

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