A simple random sample of 25 postal employees is used to test if the average tim

Question

A simple random sample of 25 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was 8 years with a standard deviation of 2 years. Assume the distribution of the time the employees have worked for the postal service is approximately normal.

a. Write the null and alternative hypothesis.

b. What assumptions are made to test the hypotheses in (a)? Comment on their validity.

c. Calculate the appropriate test statistic.

d. Is there a significant difference in the mean number of years that postal workers work at the postal service now as compared to the past (use a=0.05)? Explain.

Explanation / Answer

n = 25

(a) Below are the null and alternate hypothesis
H0: mu = 8
H1: mu not equals to 8

b)
Here assumption of normal distribution is used. Though it is approximately normal we consider it as normal and apply the central limit theorem.

c)
Test statistics, t = (7.5 - 8)/2 = -0.25

d)
p-value = 0.40235*2 = 0.804714894

As p-value is greater than the significance level of 0.05 we fail to reject the null hypothesis.

This means there are not significant evidence to conclude that the mean service time is different from 8 years.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.