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 61 employees was selected. The average age in the sample was 45 years with a sample standard deviation of 16 years. Let  = .05. Using the critical value and the p-value approaches, test to determine whether or not the mean age of all employees is significantly more than 40 years.

Answer 1

Answer:

Step-by-step explanation:

In the past, mean of age of employees

i.e. $\mu = 40$

Recently sample was taken

n = sample size = 60

Mean of sample = 45

Std dev of sample s = 16

$H_0: \bar x = 40\\H_a: \bar x >40$

(Right tailed test)

Since only population std deviation is known we can use t test only

Std error = $\frac{s}{\sqrt{n} } \\=\frac{16}{\sqrt{61} } \\=2.049$

Mean difference = 45-40 =5

Test statistic t=$\frac{5}{2.049} \\=2.441$

df = 60

p value =0.008739

Since p < 0.05 we reject null hypothesis

The mean age has increased.