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 96 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 sequals5.6 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 estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).

Step-by-step explanation:

Our sample size is 96.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

Then, we need to subtract one by the confidence level and divide by 2. So:

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 95 and 0.025 in the t-distribution table, we have .

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

Now, we multiply T and s

For the lower end of the interval, we subtract the mean by M. So

For the upper end of the interval, we add the mean to M. So

The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).

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step-by-step explanation:

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