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 11 years. A survey of 85 companies reported in The Wall Street Journal found a sample mean tenure of 10.3 years for CEOs with a standard deviation of s = 5 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 = 0.01 . Your hypotheses are: H o : μ ≥ 11 H a : μ < 11 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) α 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 11. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 11. The sample data support the claim that the population mean is less than 11. There is not sufficient sample evidence to support the claim that the population mean is less than 11.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 11
Alternative Hypothesis: μ < 11

Rejection Region
This is left tailed test, for α = 0.01 and df = 84
Critical value of t is -2.372.
Hence reject H0 if t < -2.372

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (10.3 - 11)/(5/sqrt(85))
t = -1.291

P-value Approach
P-value = 0.1
As P-value >= 0.01, fail to reject null hypothesis.

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 11.

There is not sufficient sample evidence to support the claim that the population mean is less than 11.