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 45 years with a standard deviation of 5 years. Assume the distribution of the population is normal let α= 0.5 A, state the null and the alterative hypothesis B, test to determine whether or not the mean age of all the employees is significantly more than 40 years.

Answer:Step-by-step explanation:In the past, mean of age of employees i.e. [tex]\mu = 40[/tex]Recently sample was takenn = sample size = 60Mean of sample = 45Std dev of sample s = 16[tex]H_0: \bar x = 40\\H_a: \bar x >40[/tex](Right tailed test)Since only population std deviation is known we can use t test onlyStd error = [tex]\frac{s}{\sqrt{n} } \\=\frac{16}{\sqrt{61} } \\=2.049[/tex]Mean difference = 45-40 =5Test statistic t=[tex]\frac{5}{2.049} \\=2.441[/tex]df = 60p value =0.008739Since p < 0.05 we reject null hypothesisThe mean age has increased.