Question

A shareholders' group is lodging a protest against your company. The shareholders group claimed that the mean tenure for a chief exective office (CEO) was at least 8 years. A survey of 117 companies reported in The Wall Street Journal found a sample mean tenure of 7.2 years for CEOs with a standard deviation of s = s = 5.7 years (The Wall Street Journal, January 2, 2007). You don't know the population standard deviation but can assume it is normally distributed.

You want to formulate and test a hypothesis that can be used to challenge the validity of the claim made by the group, at a significance level of α = 0.02 α = 0.02 . Your hypotheses are: H o : μ = 8 H o : μ = 8 H a : μ < 8 H a : μ < 8 What is the test statistic for this sample? test statistic = (Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)  

The p-value is...

• less than (or equal to) αα
• greater than α

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 8.
• The sample data support the claim that the population mean is less than 8.
• There is not sufficient sample evidence to support the claim that the population mean is less than 8.

Answer 1

Solution:

The test statistic is:

The p-value is:

The excel function to find the p-value is:

Where:

-1.518 is the test statistic, 116 is the degrees of freedom, 1 means a one-tailed test.

The p-value is...

Answer: greater than .

This test statistic leads to a decision to...

Answer: fail to reject the null hypothesis

As such, the final conclusion is that...

Answer:

There is not sufficient sample evidence to support the claim that the population mean is less than 8.