Consider the following hypothesis test:
$$H_0: \mu \le 75$$
$$H_a: \mu > 75$$
A random sample of 100 observations yields a sample mean of 80. The population standard deviation is 30.
a. What is the value of the test statistic?
Note: Round final answer to 3 decimal places.
Test statistic:
b. Find the p-value.
Note: Do not round the p-value when selecting the interval.
$$p-value < 0.01$$
$$0.01 \le p-value < 0.025$$
$$0.025 \le p-value < 0.05$$
$$0.05 \le p-value < 0.10$$
$$p-value \ge 0.10$$
c. What is the conclusion to the hypothesis test at the 10% significance level?
Reject $$H_0$$, the population mean is greater than 75.
Reject $$H_a$$, the population mean is not greater than 75.
Do not reject $$H_0$$, the population mean is greater than 75.