Question

Corporate sustainability of CPA firms. Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 6.12 (p. 339). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms.

The data (where higher point values indicate a higher level of support for sustainability) are saved in the accompanying file. The CEO of a

CPA firm claims that the true mean level of support for sustainability is 75 points.

a. Specify the null and alternative hypotheses for testing this claim.

b. For this problem, what is a Type I error? A Type II error?

c. The XLSTAT printout shown above gives the results of the test. Locate the test statistic and p-value on the printout.

d. At α = .05, give the appropriate conclusion.

e. What assumptions, if any, about the distribution of support levels must hold true in order for the inference derived from the test to be valid? Explain.

Short answer

a. The null and alternative hypotheses for the testing of the CEO’s claim are:

H₀: μ = 75 Against H₀: μ ≠ 75.

b. A Type I error occurs when one rejects the CEO’s claim; in fact, it is true.

A Type II error occurs when one is unable to reject the CEO’s claim; when it is false.

c. The statistic for the hypothesis from the provided output is: z = -8.4920.

The p-value for the test isp< 0.0001.

d. Reject the CEO’s claim that the true mean level of support for sustainability is 75 points.

e. The assumption required to use the z-test is the sample size is sufficiently large, and the population standard deviation is known.

Step-by-step solution

Given information

The data on the level of support for corporate sustainability for 992 managers at CPA firms is provided.

Need to test the CEO’s claim that the true mean level of support for sustainability is 75 points.

Specifying the null and alternative hypothesis

a.

let μrepresents the true mean level of support for sustainability.

The null and alternative hypotheses for the testing of the CEO’s claim are:

H₀: μ = 75 Against H₀:μ ≠ 75.

Identifying the types of errors in hypothesis testing

b.

A Type I error occurs when one rejects the CEO’s claim; in fact, it is true.

A Type II error occurs when one is unable to reject the CEO’s claim; when it is false.

Identifying the types of errors in hypothesis testing

The statistic for the hypothesis from the provided output is: z = -8.4920.

The p-value for the test is p< 0.0001.

Drawing the conclusions

d.

The p-value for the hypothesis test is less than the significance level α = 0.05.

Therefore, reject the CEO’s claim that the true mean level of support for sustainability is 75 points.

Checking the underlying assumptions

e.

The assumption required to use the z-test are sample size is sufficiently large, and the population standard deviation is known.

Here the sample size is too large; therefore, the assumption to use the z-test is satisfied.