A researcher believes that trout spawning in Wisconsin is lower this year than in prior years. Historical data tells us that the average number of trout per spawning pool is 98.6 fish with a standard deviation of 14.3. The researcher takes a random sample of 45 trout spawning pools in Wisconsin and records an average of 89.5 fish. Use this information to perform the appropriate steps of a hypothesis test.

(a) Select all correct formulations of the Null Hypothesis for testing the researcher's claim. (3pts)

I. H0: Trout spawning is lower this year than in prior years. ii. H0: Average_trout = 98.6 iii. H0: Average_trout < 98.6 iv. H0: Average_trout > 98.6 v. H0: Trout spawning is the same this year as in prior years.

(b) Select all correct formulations of the Alternative Hypothesis for testing the researcher's claim. (3pts)

I. Ha: Trout spawning is lower this year than in prior years. ii. Ha: Average_trout = 98.6 iii. Ha: Average_trout < 98.6 iv. Ha: Average_trout > 98.6 v. Ha: Trout spawning is the same this year as in prior years

(c) Calculate the appropriate test statistic and p-value. (8pts)

(d) State your conclusion in the context of the problem. (3pts)

(e) State what error (Type I or Type II) might have been committed and interpret that error in the context of the problem. (3pts)

(f) If instead, the researcher wished to determine if the average number of trout in Wisconsin spawning pools is different from 98.6, what would their null and alternative hypothesis be? (3pts)