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-7.87 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
(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 a-0.01, what is your conclusion?

Answer 1

Following are the responses to the given question:

Explanation:

Hypotheses are:

`H_0: \mu \geq 9\\\\H_a: \mu < 9`

It is a left-tailed test, as well as the t distribution must be used because the standard deviation is unknown.

Testing statistic:

`t=\frac{\bar{x}-\mu}{(s)/(√(n))} = (7.87-9)/((6.38)/(√(84)))=-1.63`

Using excel function
`=T.DIST(-1.63,84-1,TRUE)`

`p-value = 0.0531 \\\\Since \ p-value = 0.0531 > 0.01:\\\\`

The hypothesis can not be rejected. It can't infer that only a CEO's average term is less than nine years.