Question

A study of the pay of corporate chief executive officers (CEOs) examined the increase in cash compensation of the CEOs of 97 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x = 6.8%, and the standard deviation of the increases was s = 45%. Is this good evidence that the mean real compensation μ of all CEOs increased that year?

Ho: μ = 0 (no increase)

Ha: μ > 0 (an increase)

Because the sample size is large, the sample s is close to the population σ, so take σ = 45%.

(a) Sketch the normal curve for the sampling distribution of x when Ho is true. Shade the area that represents the P-value for the observed outcome x = 6.8%. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Calculate the P-value. (Round your answer to four decimal places.)

c) Is the result significant at the a = 0.05 level? Do you think the study gives strong evidence that the mean compensation of all CEOs went up?

Reject the null hypothesis, there is significant evidence that the mean compensation of all CEOs went up.

Reject the null hypothesis, this is not significant evidence that the mean compensation of all CEOs went up.

Fail to reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up.

Fail to reject the null hypothesis, there is significant evidence that the mean compensation of all CEOs went up.

Answer 1

Answer)

S.d = 45%

Claimed mean = 6.8%

Observed mean = 6.8%

As the population standard deviation is known, we can use standard normal z table to conduct the test.

Test statistics z = (observed mean - claimed mean)/(s.d/√n)

Z = 0

From z table, p(z>0) = 0.5

Therefore the required p-value is 0.5.

As the obtained p-value is greater than the given significance level 0.05

We fail to reject the null hypothesis.

Fail to reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up.