Question

A group of shareholders claimed that the mean tenure for a CEO was at least nine years. A survey of 81 companies found a sample mean tenure of 7.9 years with a standard deviation of 6.4 years. Using the p-value approach, perform the appropriate test at ?=0.10.

Answer 1

1stly make the hypothesis

H₀ = mu 9 , H1 = mu < 9

sample mean (x̄) = 7.9 , sample standard deviation = 6.4 and n = 81

here we have sample standard deviation this means we use t - test

t - test = ( x̄ – μ) / (s / √n)

= (7.9 - 9) / (6.4 / √81)

= (-1.1) / (6.4 / 9)

= (-1.1) / (0.711)

= - 1.546

now check the value in t-table with degree of freedom is 80 i.e (n-1)

0.5 P(t - 2.5) 0.01

now we get the range of p-value is 0.5 P(t - 2.5) 0.01

as this is one tail t-test (left tail) we have to find out the area to the left

now alpha = 0.10 for conclusion

0.5   P-value  0.01   0.10

Reject H₀

our claim that mean tenure for a CEO is less then 9 years

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