Question

A major business magazine published the results of a survey conducted of CEOs. Responses were received from 216 CEOs for this random sample. The survey used a scale of 1 to 5 where a value of 1 indicated they were extremely dissatisfied and 5 indicated extremely satisfied. The survey results had a mean response of 3.78 with a standard deviation of 1.65. Test the hypothesis at the .01 level that the mean response of all CEOs is equal to 3.9.

What is the alternative hypothesis (H1)?

Select one:

a. H1: The mean is not equal to 3.9.

b. H1: The mean is greater than 3.9.

c. H1: The mean is not equal to 3.78.

d. H1: The mean is less than 3.9.

What is the critical value for step 2?

Select one:

a. -2.33

b. 1.96, -1.96

c. 2.33

d. 2.575, -2.575

What is the value of the calculated test statistic value (step 3)?

Select one:

a. -1.07

b. .073

c. -1.65

d. 0.12

What is your decision and what does it indicate (steps 4 and 5)?

Select one:

a. Fail to reject H0. The mean does not equal 3.9.

b. Reject H0. The mean is less than 3.9.

c. Reject H0. The mean does not equal 3.9.

d. Fail to reject H0. The mean equals 3.9.

Answer 1

Q1) As we are testing the hypothesis here whether mean is equal to 3.9, the null and the alternate hypothesis here would be given as:

Therefore a) is the correct answer here:
a. H1: The mean is not equal to 3.9.

Q2) As we are testing it at 0.01 level of significance, and the same size is large enough to apply the Z test, we get from the standard normal tables that:

P( - 2.575 < Z < 2.575 ) = 1 - 0.01 = 0.99

Therefore 2.575 are the critical values here.

Therefore d is the correct answer here. d. 2.575, -2.575 is the correct answer here.

Q3) The test statistic value here is computed as:

Therefore a) -1.07 is the correct answer here.

Q4) As the test statistic value lies within the critical values range, we cannot reject the null hypothesis here. The mean is thus equal to 3.9 ( retaining the null hypothesis ) d. Fail to reject H0. The mean equals 3.9. is the correct answer here.