To test H0: = 45 versus H1: 45, a simple random sample of size n = 40 is obtained. (a) Does the

To test H0: µ = 45 versus H1: µ ≠ 45, a simple random sample of size n = 40 is obtained.

(a) Does the population have to be normally distributed to test this hypothesis by using the methods presented in this section? Why?

(b) If x̄ = 48.3 and s = 8.5, compute the test statistic.

(c) Draw a t-distribution with the area that represents the P-value shaded.

(d) Determine and interpret the P-value.

(e) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, will the researcher reject the null hypothesis? Why?

(f) Construct a 99% confidence interval to test the hypothesis.