Question

A sample of 30 commuters in the area of a certain city yielded the accompanying commute times, in minutes. Preliminary data analyses indicate that the t-interval procedure can reasonably be applied. Find and interpret a 95% confidence interval for the mean commute time of all commuters in the area of the city (note: xbar = 28.20 minutes and s = 9.39 minutes)

Answer 1

Solution :

Given that,

= 28.20

s = 9.39

n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,29 =2.045

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

= 2.045 * (9.39 / 30)

= 3.51

Margin of error = 3.51

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

- E < < + E

28.20 - 3.51 < < 28.20 + 3.51

24.69 < < 31.71

(24.69, 31.71)