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 ≤ 23 H1: μ > 23 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 when z > 1.645 Reject H0 when z ≤ 1.645 What is the value of the test statistic? (Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Fail to reject H0 e-1. What is the p-value? (Round your answer to 4 decimal places.) e-2. Interpret the p-value? (Round your final answer to 2 decimal places.)

Answer 1

Solution :

= 23

= 24

= 3

n = 44

This is the one tailed test .

Right tail test

The null and alternative hypothesis is ,

H₀ :   ≤ 23

H_a : > 23

Test statistic = z

= ( - ) / / n

= (24 - 23) / 3 / 44

= 2.21

z= 2.21 > z_c​ =1.64, it is then concluded that

the null hypothesis rejected .

p(Z >2.21 ) = 1-P (Z < 2.21 ) = 0.0135

P-value = 0.0135

= 0.05  

p= 0.0135 < 0.05, it is concluded that the null hypothesis is rejected.

There is enough evidence to claim that the population mean μ is greater than 23, at the 0.05 significance level.