Question

A random sample of 18 residents looked at how many miles residents were commuting (two ways) to get to work and back. The survey found that the average number of miles they commute had a mean of 23.2 miles round trip, and a standard deviation of 18.1 miles.

a) Calculate a 95% confidence interval for the true mean commute distances of the residents.

b) Interpret your interval from part (a)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 23.2

Population standard deviation =    = 18.1

Sample size = n = 18

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 18.1 /  18 )

= 8.36

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

- E < < + E

23.2 - 8.36 <   < 23.2 + 8.36

14.84 <   < 31.46

( 14.84 , 31.46 )

The 95% confidence interval estimate of the population mean is : - ( 14.84 , 31.46 )

( b ) Interpret : - About The 95% confidence interval for the true mean commute distances of the residents .