In the year 2014, a sample of 29 college music students had a sample mean math ACT score of 21.1 with a sample standard deviation of 5.7. You wish to use these results to address the following statistical question: Do the data provide sufficient evidence to indicate that the mean math ACT score for all college music students in 2014 differed from the national average of 20.9?You will answer this question by testing the null hypothesis H₀: = 20.9 against the alternative hypothesis H_a: 20.9.Use a significance level of = 0.05.

(a - 10 pts.) Compute the value of the test statistic. Show the formula and all computations.

(b - 10 pts.) Identify the rejection region. You may use a diagram or picture if you want. Be sure to explain how you obtain any numbers that you use.

(c - 8 pts.) Draw a conclusion about math ACT scores for college music students, and express it meaningfully in words. Fully justify this conclusion.