uestion 1 A company and its union are contemplating changes to the company pensi
ID: 3062732 • Letter: U
Question
uestion 1 A company and its union are contemplating changes to the company pension plan. The company representative claims that the average number of years of service for the employees of the company is greater than 20. The union disagrees and claims that the representative's claim is too high. A sample of 24 employees was selected. The number of years of service for each of these employees is as follows: 262018 22 19102524 2026 19 21 2225 19 22 2117 20 23 2228 20 a) Test the claim of the company representative at the 4% level of significance. Clearly show the steps of the hypothesis test that you use, and express your final conclusion using a clear English sentence. (12 marks) b) Determine the 98% confidence limit for the number of years of service for employees in the company. (3 marks)Explanation / Answer
a)
Below are the null and alternate hypothesis:
H0: mu <= 20
H1: mu > 20
From the given data we have
n = 24
Mean = 21.5
std. dev. = 3.8448
Test statistics, t = (21.5 - 20)/(3.8448/sqrt(24))
t = 1.9113
p-value = 0.0343
As p-value is less than the significance level of 0.04, we reject the null hypothesis.
This means there are significant evidence to conclude that average numer of years of service for the employees of the company is greater than 20.
b)
CI for 98% n 24 mean 21.5 t-value of 98% CI 2.4999 std. dev. 3.8448 SE = std.dev./sqrt(n) 0.78482 ME = t*SE 1.96194 Lower Limit = Mean - ME 19.53806 Upper Limit = Mean + ME 23.46194 98% CI (19.5381 , 23.4619 )Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.