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 92

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 overbarxequals=19.9

mpg and

s=6.8

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

​(Round to one decimal place as needed. Use ascending​ order.)

Interpret this interval. Choose the correct answer below.

A.There is a

0.95

probability that the true mean highway mpg for SUVs falls in this range.

B.One can conclude with

95​%

confidence that the true mean highway mpg for SUVs is in this range.

C.One can conclude with

95​%

confidence that the sample mean highway mpg for SUVs is in this range.

D.One can conclude that the true mean highway mpg for SUVs will fall in this range

95​%

of the time.

Answer 1

Solution :

degrees of freedom = n - 1 = 92 - 1 = 91

t/2,df = t0.025,91 = 1.986

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

= 1.986 * (6.8 / 92)

Margin of error = E = 1.4

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

  ± E  

= 19.9 ± 1.4

= ( 18.5 mpg, 21.3 mpg )

B.One can conclude with 95​% confidence that the true mean highway mpg for SUVs is in this range