Question

As a​ follow-up to a report on gas​ consumption, a consumer group conducted a study of SUV owners to estimate the mean mileage for their vehicles. A simple random sample of 80 SUV owners was​ selected, and the owners were asked to report their highway mileage. The results that were summarized from the sample data were x overbarequals19.6 mpg and sequals6.6 mpg. Based on these sample​ data, compute and interpret a 95​% confidence interval estimate for the mean highway mileage for SUVs. The 95​% confidence interval is mpg---mpg

Answer 1

Solution :

Given that,

= 19.6

s =6.6

n =80

Degrees of freedom = df = n - 1 = 80 - 1 = 79

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,79 = 1.990

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

=1.990 * (6.6 / 80) =1.4684

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

- E < < + E

19.6 - 1.4684 < < 19.6+ 1.4684

18.1316 < < 21.0684

( 18.1316 , 21.0684)