Question

A company has 189 accountants. In a random sample of 50 of them, the average number of overtime hours worked in a week was 9.7 and the sample standard deviation was 6.2 hours.

a) Find a 95% confidence interval of the average number of overtime hours worked by each accountant in this company during that week.

b) Find a 99% confidence interval of the total number of overtime hours worked by each accountant in this company during that week.

Answer 1

Solution :

Given that,

sample size = n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

a)

t _/2,df = = 2.010

Margin of error = E = t_/2,df * (s /n)

= 2.010 * (6.2 / 50)

Margin of error = E = 1.8

The 95% confidence interval estimate of the population mean is,

- E < < + E

9.7 - 1.8 < < 9.7 + 1.8

7.9 < < 11.5

(7.9 , 11.5)

b)

t _/2,df = 2.680

Margin of error = E = t_/2,df * (s /n)

= 2.680 * (6.2 / 50)

Margin of error = E = 2.3

The 99% confidence interval estimate of the population mean is,

- E < < + E

9.7 - 2.3 < < 9.7 + 2.3

7.4 < < 12.0

(7.4 , 12.0)