Question

A sample of 60 observations is selected from a normal population. The sample mean is 37, and the population standard deviation is 8.

Conduct the following test of hypothesis using the 0.10 significance level.

H₀ : μ ≤ 36

H₁ : μ > 36

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

One-tailed test or Two-tailed test

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

(Reject or Accept)  H₀ and  (accept or 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?

Reject or Do not reject  H₀.

There is  (enough or not enough) evidence to conclude that the population mean is greater than 36.

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

Answer 1

Solution

= 36

=37

=8

n = 60

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :   < 36

Ha : > 36

Test statistic = z

= ( - ) / / n

= (37-36) / 8 / 60

= 0.97

Test statistic = z = 0.97

The critical value = 1.282

P(z > 0.97 ) = 1 - P(z < 0.97) = 1 - 0.8340

P-value =0.166

= 0.10

P-value >

0.166 > 0.10

Fail to reject the null hypothesis .

There is insufficient evidence to conclude that the population mean is greater than 36