Question

A sample of 46 observations is selected from a normal population. The sample mean is 39, and the population standard deviation is 9.

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

H₀ : μ ≤ 38

H₁ : μ > 38

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 38.

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

__________________

Answer 1

a) As we are testing here whether the mean is more than 38, therefore this is a case of a one tailed test here.

b) For 0.1 level of significance, we have from the standard normal tables:
P(Z > 1.282) = 0.1

Therefore the decision rule here is given as:
Reject H0 if z > 1.282

c) The test statistic here is computed as:

Therefore 0.7536 is the test statitistic value here.

d) As the test statistic value is less than the critical z value, therefore Do not reject H0 is the correct answer here. Therefore is not enough evidence here to conclude that the population mean is greater than 38.

e) As this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z > 0.7536) = 0.2255

Therefore 0.2255 is the required p-value here.