Suppose that you are to conduct the following hypothesis test
$H_0: \mu = 510$
$H_1: \mu \neq 510$
Assume that you know that $\sigma = 75$, $n = 42$, $\bar{x} = 498$, and take $\alpha = 0.01$. Draw the sampling distribution, and use it to determine each of
the following:
A. The value of the standardized test statistic
Note: For the next part, your answer should use interval notation. An answer of the form $(-\infty, a)$ is expressed $(-\infty, a)$, an answer of the
form $(b, \infty)$ is expressed $(b, \infty)$, and an answer of the form $(-\infty, a) \cup (b, \infty)$ is expressed $(-\infty, a)\cup(b, \infty)$.
B. The rejection region for the standardized test statistic
C. The p-value is
D. Your decision for the hypothesis test:
A. Do Not Reject $H_0$
B. Reject $H_0$
C. Do Not Reject $H_1$
D. Reject $H_1$.
