Question

In the past the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. 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 average age in the sample was 42.5 years with a sample standard deviation of 5 years. Using a significance level of α = .01, do the sample data provide support for the contention that there has been a significant increase in the average age of all the employees? Do a complete and appropriate hypothesis test. Assume that the distribution of the population is normal.

Step 1 (Hypotheses)

H₀:  (Click to select)nx-barσμπps  (Click to select)=≠≤>≥<  

H_A:  (Click to select)μx-barπpσsn  (Click to select)=≠≤>≥<  

Step 2 (Decision rule)

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is (Click to select)+-± . (report your answer to 3 decimal places, using conventional rounding rules)

Step 3 (Test statistic)

Using the sample data, the calculated value of the test statistic is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Step 4 (Evaluate the null hypothesis)

Should the null hypothesis be rejected?  (Click to select)yesno

Step 5 (Practical conclusion)

Can you conclude that there has been a significant increase in the average age of all employees?  (Click to select)yesno

Using only the appropriate statistical table in your textbook, what is the most accurate statement you can make about the p-value of this hypothesis test?

Answer: (Provide a brief one-sentence statement about the approximate p-value of this hypothesis test using the appropriate statistical table in your textbook)

Answer 1

Step1:

Step 2:

ndf = n - 1 = 25 - 1 = 24

One Tail - Right side test.

From Table, critical value of t is given by:

t > 2.4922

Step 3:

Test statistic is:

t = (42.5 - 40)/1

= + 2.50

So,

test statistic is:

t = + 2.50

Step 4:

Since calculated value of t = 2.50 is greater than critical value of t = 2.4922, the difference is signiicant. Reject null hypothesis.

So,

Answer is:

Yes

Step 5:

Answer is:

Yes

Step 7:

t score = 2.50

ndf = 24

One Tail =- Right test

By Technology, p- value = 0.0098

The data support the claim that there has been an increase in the average age of all the employees.