Question

eBook A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least eleven years. A survey of companies reported in the Wall Street Journal found a sample mean tenure of 10.68 years for CEOs with a standard deviation of s 7.21 years. a. Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. Ho Select your answer- 11 Ha Select your answer-11 b. Assume 80 companies were included in the sample. What is the p-value for your hypothesis test? Enter negative value as negative number (to 3 decimals) t-value p-value l -select your answer- C. At α = 0.01, what is your conclusion? -select your answer- the null hypothesis. wel-select your answer-▼| enough evidence to disprove the shareholder group's claim

Answer 1

To Test :-

Mean tenure for CEO was atleast 11 years

H₀ :-

H₁ :- $\mu \geq 11$

Part b)

t value

$t = ( \bar{X} - \mu ) / (S /\sqrt{n})$

$t = ( 10.68 - 11) / (7.21/\sqrt{80})$

Looking for the t value in t table across n-1 degree of freedom i.e 80 - 1 = 79 DF for 1 tailed

we can see that | t | = 0.397 lies between values 0.000 & 0.678 that has P value between 0.50 & 0.25

0.25 < P value < 0.50

P Value = 0.346 calculated on excel

Part c)   $\alpha = 0.01$

Reject null hypothesis if $t > t_{\alpha , n-1}$

$t_{\alpha , n-1} = t_{0.01, 80-1} = 2.374$

- 0.397 < 2.374, hence we fail to reject null hypothesis

Conclusion :- Accept null hypothesis

$\mu < 11$