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 123 companies reported in The Wall Street Journal found a sample mean tenure of 6.9 years for CEOs with a standard deviation of s=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=0.01α=0.01. Your hypotheses are:

      Ho:μ≥8Ho:μ≥8
      H1:μ<8H1: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 αα

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

To Test :-

Ho:μ≥8
H1:μ<8

Test Statistic :-


t = -2.4897

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.4897 ) = 0.0071
Reject null hypothesis if P value < level of significance
P - value = 0.0071 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 8.