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

a) Does the population have to be normally distributed to test this hypothesis? Why?

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

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

d) Determine the P-value.

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