A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be  = 2.05 years, with sample standard deviation s = 0.82 years (based on information from the book Coyotes: Biology, Behavior, and Management, edited by M. Bekoff, Academic Press). However, it is thought that the overall population mean age of coyotes is μ = 1.75 years. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.
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 “conservative” answer.