Question

In the past, the average age of TXU employees has been 40 years. Recently, TXU has been hiring older people. In order to determine whether there has been an increase in the average age of all the employees, a sample of 25 employees was selected. The sample average age was 45 years with a standard deviation of 5 years. Assume α = .05. What is the the p value for this test? What is the critical value for this test?

Answer 1

Given that population mean = 40, sample mean=45, sample standard deviation =5 and sample size n = 25

t test statistic =

degree of freedom = n-1 = 25-1 = 24

using t distribution table, check t value in left most column and df value in the top row, selecting the intersecting cell, we get

p value = 0.0000

For t critical, check degree of freedom (24) in the distribution with alpha level 0.05

we get, t critical = 1.711

p value is less than significance level 0.05, rejecting the null hypothesis

t statistic is greater than t critical, again rejecting the null hypothesis