Question

A sample of 30 observations is selected from a normal population. The sample mean is 22, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.01 significance level. H0: μ ≤ 20 H1: μ > 20

(A) Is this a one- or two-tailed test?

(B) What is the decision rule?

(C) What is the value of the test statistic? (Round your answer to 2 decimal places.)

(D) What is your decision regarding H₀?

(E) What is the p-value? (Round your answer to 4 decimal places.)

(F) Interpret the p-value? (percentage wise) (Round your final answer to 2 decimal places.)

Answer 1

A. As alternative hypothesis is having greater than sign, it is right tailed test. So one-tailed test.

B. The z-critical value for a right-tailed test, for a significance level of α=0.01 is

zc​=2.33

Graphically

C.Here population standard deviation is known so we will use test statistics

D. As test statistics falls in the rejection region we reject the null hypothesis

E. P value is