Question

A consumer group conducted a study of SUV owners to estimate the mean highway mileage for their vehicles. A simple random sample of 91 SUV owners was selected, and the owners were asked to report their highway mileage. The following results were summarized from the sample data.

Sample Mean = 21.3 mpg

Standard Deviation = 6.3 mpg

Based on these sample data, compute and interpret a 90% confidence interval estimate for mean the highway mileage for SUVs.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 21.3

sample standard deviation = s = 6.3

sample size = n = 91

Degrees of freedom = df = n - 1 = 90

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,90 = 1.662

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

= 1.662 * ( 6.3/ 91)

= 1.098

The 90% confidence interval estimate of the population mean is,

- E < < + E

21.3 - 1.098 < < 21.3 + 1.098

20.202 < < 22.398

(20.202 , 22.398)

One can conclude with 90% confidence that the true mean Highway mpg for SUVs for this range.