Question

Suppose you want to know if the average age of CEO’s at fortune 500 companies has increased in recent years. In 2010 you took a sample of 30 CEO’s and find their average age is 47 with a sample variance of s 2 2 = 36. In 2016 you took a sample of 25 CEO’s and find their average age is 50 with a sample variance of S 1 2 = 25. Assume the degrees of freedom is 42

What is the 90% confidence interval for the population difference between 2016 and 2010 CEO ages, i.e. μ ¯ 1 − μ ¯ 2

Using the information above, assume you want to test for whether the average age of CEO's has increased. What is the null and alternative hypothesis?

Assume the hypothesis test in question 18 was the following:

H 0 : D = 0 ; H A : D ≠ 0

What are the critical values for the 90, 95, and 99% levels?

What is the test statistic for the above hypothesis test?

Answer 1

1) df = 42

At 90% confidence level, the critical value is t^* = 1.682

The 90% confidence interval is

2)

  

3) df = 42

At 90% confidence level, the critical values are +/- t_0.05 = +/- 1.682

At 95% confidence level, the critical values are +/- t_0.025 = +/- 2.018

At 99% confidence level, the critical values are +/- t_0.005 = +/- 2.698

The test statistic is