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 9 years. A survey of 115 companies reported in The Wall Street Journal found a sample mean tenure of 8.8 years for CEOs with a standard deviation of s = 5.1 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 = 0.05 . Your hypotheses are: H o : μ ≥ 9 H a : μ < 9 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.)

Answer 1

x = 8.8, s = 5.1, n = 115, μ = 9

Level of significance = 0.05

Degrees of freedom: df = n-1 = 115-1 = 114

H_o: μ ≥ 9, H_a: μ < 9

Test statistic = (x-μ)/(s/n^0.5) = (8.8-9)/(5.1/115^0.5) = -0.421

p-value (Using Excel function T.DIST.2T(test statistic, df, cumulative)) = T.DIST(-0.421,114,TRUE) = 0.337

Since p-value is greater than 0.05, we do not reject the null hypothesis and conclude that μ ≥ 9.

So, mean tenure for a chief exective office (CEO) was at least 9 years.