Question

2. A firm would like to know the average time it takes its employees to commute to work. The firm takes a sample of 37 workers and finds a sample mean of 38 minutes, with a sample standard deviation of 14 minutes. Construct a 99% confidence interval for the population mean.

a) State the critical value:

b) Calculate the margin of error (round to the thousandths place):

c) State the lower and upper values of the confidence interval:

Answer 1

c )solution

Given that,

= 38

s =14

n = 37

Degrees of freedom = df = n - 1 =37 - 1 = 36

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,36 =2.719    ( using student t table)

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

= 2.719 * (14 / 37) = 6.258

The 99% confidence interval is,

- E < < + E

38 - 6.258 < < 38+6.258

(31.742 , 44.258)

lower bound 31.742

upper bound 44.258