Problem 8.25 In order to test H0 : 10 against H1 : < 10 a researcher computes the observed values x and

Problem 8.25 In order to test H0 : µ ≥ 10 against H1 : µ < 10 a researcher computes the observed values x and s of the sample mean and sample standard deviation of random sample of size n = 12 taken from a normal distribution N(µ, σ2). Compute the P-value of the test if the observed values x and s are:

(a) x = 9, s = 3.0.

(b) x = 8.5, s = 3.0.

(c) x = 8.5, s = 2.5.

(d) For which of the computed P-values in parts (a), (b), and

(c) would the null hypothesis be rejected at the 5% level of significance?