According to an estimate, 2 years ago the average age of all CEOs of medium-sized companies in the United States was 58 years. Jennifer wants to check if this is still true. She took a random sample of 70 such CEOs and found their mean age to be 54 years with a standard deviation of 6 years. Using the 1% significance level, can you conclude that the current mean age of all CEOs of medium-sized companies in the United States is different from 58 years?

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 58

For the alternative hypothesis,

µ ≠ 58

This is a two tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 70

Degrees of freedom, df = n - 1 = 70 - 1 = 69

t = (x - µ)/(s/√n)

Where

x = sample mean = 54

µ = population mean = 58

s = samples standard deviation = 6

t = (54 - 58)/(6/√70) = - 5.58

We would determine the p value using the t test calculator. It becomes

p < 0.0000

Since alpha, 0.01 > than the p value, then we would reject the null hypothesis. Therefore, at a 1% significance level, we can conclude that the current mean age of all CEOs of medium-sized companies in the United States is different from 58 years.