Question

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive officer (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.67 years for CEOs with a standard deviation of s = 6.38 years. (a) Choose the correct hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. H0: μ - Select your answer - years Ha: μ - Select your answer - years (b) Assume that 85 companies were included in the sample. What is the p value for your hypothesis test? If required, round your answer to four decimal places. (c) At α = 0.01, what is your conclusion? We - Select your answer - the null hypothesis. We - Select your answer - conclude that the mean tenure for a CEO is shorter than nine years.

Answer 1

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0:µ ≥ 9

For the alternative hypothesis,

Ha:µ < 9

This is a left tailed test.

b) Since the population standard deviation is not given, the distribution is a student's t.

Since n = 85,

Degrees of freedom, df = n - 1 = 85 - 1 = 84

t = (x - µ)/(s/√n)

Where

x = sample mean = 7.67

µ = population mean = 9

s = samples standard deviation = 6.38

t = (7.67 - 9)/(6.38/√85) = - 1.92

We would determine the p value using the t test calculator. It becomes

p = 0.029

c) α = 0.01

Since α, 0.01 < the p value, 0.029, then we would fail to reject the null hypothesis. Therefore, At a 1% level of significance, there was no significant evidence that the the mean tenure for a CEO is shorter than nine years.