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 90 SUV owners was​ selected, and the owners were asked to report their highway mileage. The results that were summarized from the sample data were bar over x =17.3 mpg and s =6.2 mpg. Based on these sample​ data, compute and interpret a 99​% confidence interval estimate for the mean highway mileage for SUVs.

The 99​% confidence interval = mpg–––– mpg. ​(Round to one decimal place as needed. Use ascending​ order.)

Interpret this interval. Choose the correct answer below.

A.There is a 0.99 probability that the true mean highway mpg for SUVs falls in this range.

B.One can conclude that the true mean highway mpg for SUVs will fall in this range 99​% of the time.

C.One can conclude with 99​% confidence that the sample mean highway mpg for SUVs is in this range.

D.One can conclude with 99​% confidence that the true mean highway mpg for SUVs is in this range

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 17.3 mpg

sample standard deviation = s = 6.2 mpg

sample size = n = 90

Degrees of freedom = df = n - 1 = 90 - 1 = 89

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,89 = 2.632

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

= 2.632 * (6.2 / 90)

Margin of error = E = 1.7

The 99% confidence interval estimate of the population mean is,

  ± E  

= 17.3  ± 1.7

= ( 15.6 mpg, 19.0 mpg )

D.One can conclude with 99​% confidence that the true mean highway mpg for SUVs is in this range