Question: The average annual salary of major league baseball players is now $1,789,556. Suppose this year a random sample of 35 major league players in Florida had an average annual salary of \(\bar{X}\) = $1,621,726 with sample standard deviation s = $591,218. Use a 1% level of significance to test the claim that the average salary for all Florida players is different from the national average.

(a) What is the null hypothesis? What is the alternate hypothesis? Will we use a left-tailed, right-tailed, or two-tailed test? What is the level of significance?

(b) What sampling distribution will we use? What is the critical value zo (or critical values ± zo)

(c) Sketch the critical region and show the critical value (or critical values).

(d) Calculate the z value corresponding to the sample statistic \(\bar{X}\) and show it’s location on the sketch of part (c)

(e) Based on your answers for parts (a) to (d), shall we reject or fail to reject (i.e., “accept”) the null hypothesis at the given level of significance \(\alpha \) ? Explain your conclusion in the context of the problem.

(f) Are the data statistically significant?