Question

8.1.14-T Question Help 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 91 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 = 19.8 mpg and s = 6.8 mpg. Based on these sample data, compute and interpret a 90% confidence interval estimate for the mean highway mileage for SUVS. The 90% confidence interval is mps- (Round to one decimal place as needed. Use ascending order.) mp3

Answer 1

Solution:

Given, , n=91

19.8 mpg, s= 6.8, Confidence level 90%

The critical value of $\alpha= 0.10$ and df=91-1 is $t_c=1.662$ .

Hence the 90% confidence interval for $\mu$ is given by,

$(\bar{x}-t_c* \frac{s}{\sqrt{n}},\bar{x}+t_c* \frac{s}{\sqrt{n}})$

=$(19.8-1.662* \frac{6.8}{\sqrt{91}},19.8+1.662* \frac{6.8}{\sqrt{91}})$

=

$\simeq (18.6,21.0)$

The 90% confidence interval is 18.6 mpg -- 21.0 mpg.

**For further queries, please comment below. Thank you.