Question

Please SHOW YOUR Calculations and formulas in Excel

A shareholder’s group, in lodging a protest, claimed that the mean tenure for a chief executive officer (CEO) was at least 9 years. A survey of companies reported in the Wall Street Journal found a sample mean tenure of ?̅= 7.27 years for CEOs with a standard deviation of 6.38 years.

1) Formulate a hypothesis that can be used to challenge the validity of the claim made by the shareholder’s group.

2) Assume that 85 companies were included in the sample. What is the p value for your hypothesis test?

3) At a level of significance of 1%, what is your conclusion?

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Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 7.27 - 9 ) / ( 6.38 / √(85) )
t = -2.5

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
t(α, n-1) = t(0.01 , 85-1) = 2.372
t > t(α, n-1) = -2.5 < 2.372
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 2.5 ) = 0.9928
Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.9928 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to conclude the claim that the mean tenure for a chief executive officer (CEO) was at least 9 years.