In Testing the Hypotheses $H _ { 0 }$ $\mu = 20$

Essay

In testing the hypotheses $H _ { 0 }$ : $\mu = 20$ . $H _ { 1 } : \mu < 20$ .
the following information was given: $\sigma = 8.1 , \quad n = 100 , \quad \bar { x } = 18.1 , \quad \alpha = 0.025$ .
a. Calculate the value of the test statistic.
b. Set up the rejection region.
c. Determine the p-value.
d. Interpret the result.