Question

A sample of 44 observations is selected from a normal population. The sample mean is 24, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level.

H0: μ ≤ 24 H1: μ > 24

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

b) What is the decision rule?

c) What is the value of the test statistic?

d) What is your decision regarding H0?

e) What is the p-value?

f) Interpret the p-value?

Answer 1

Given:

Sample size, n = 44

Sample mean, = 24

Population standard deviation, = 3

Significance level, = 0.05

Hypothesis test :

H0 : μ ≤ 24

H1 : μ > 24

a) This is a one - tailed test.

b) Decision rule :

For 0.05 significance level, critical value of z-test is 1.645.

If z > 1.645, then reject the null hypothesis, H0. Otherwise do not reject null hypothesis, H0

Hence at 5% significance level, we have significant evidence to conclude that is greater than 24.