Question

A sample of 36 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level.

H₀: μ ≤ 20

H₁: μ > 20

a). What is the decision rule? (Round your answer to 2 decimal places.)

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

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

Answer 1

Solution :

= 20

= 21

= 5

n = 36

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   ≤ 20

H_a : > 20

The significance level is α=0.05,

The critical value for a right-tailed test is z_c​=1.64.

The rejection region for this right-tailed test is R = (z:z >1.64)

Test statistic = z

= ( - ) / / n

= (21 - 20) /5 / 36

= 1.20

P(z >1.20 ) = 1 - P(z < 1.20 ) = 0.1151

P-value = 0.1151

= 0.05  

p=0.1151≥0.05, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population meanμ is greater than 20, at the 0.05 significance leveL