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 97 companies reported in The Wall Street Journal found a sample mean tenure of 9.2 years for CEOs with a standard deviation of s=4.9 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. Your hypotheses are:

      Ho:μ≥11
      Ha: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.)

Answer 1

Solution :

= 11

=9.2

s =4.9

n = 97

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   ≥ 11

H_a : < 11

Test statistic = t

= ( - ) / s / n

= (9.2-11) / 4.9 / 97

= −3.618

Test statistic = t=  −3.62

P-value =0.0002

= 0.02

P-value <

0.0002 < 0.02

Reject the null hypothesis .

There is sufficient evidence to suggest that