Question

A sample of 71 observations is selected from a normal population. The sample mean is 24, and the population standard deviation is 8.

Conduct the following test of hypothesis using the 0.05 significance level.

H₀ : μ ≤ 23

H₁ : μ > 23

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

(Click to select)  One-tailed test  Two-tailed test

b. What is the decision rule? (Round the final answer to 3 decimal places.)

(Click to select)  Reject  Accept  H₀ and  (Click to select)  accept  reject  H₁ when z >  .

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

Value of the test statistic

d. What is your decision regarding H₀?

(Click to select)  Reject  Do not reject  H₀.

There is  (Click to select)  not enough  enough   evidence to conclude that the population mean is greater than 23.

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

Answer 1

Solution :

Given that ,

= 23  

= 24

= 8

n = 71

The null and alternative hypothesis is ,

H0 :   23

H1 : > 23

This is the right tailed test .

= 0.05  

Z = Z 0.05 = 1.645

Z > 1.645

The critical value = 1.645

Test statistic = z

= ( - ) / / n

= ( 24 - 23 ) / 8 / 71

= 1.05

The value of the test statistic = 1.05

1.05 < 1.645

Test statistic < critical value

Reject the null hypothesis .

There is sufficient enough  evidence to conclude that the population mean is greater than 23.

P - value = P(Z > 1.05) = 1- P (Z < 1.05 )

= 1 - 0.8531

= 0.1469

The P-value = 0.1469