Final answer:
To compute a 99% confidence interval estimate for the mean highway mileage for SUVs based on the sample data x = 19.4 mpg and s = 6.2 mpg, we can use the formula: CI = x ± z * (s/√n). The 99% confidence interval for the mean highway mileage for SUVs is (16.887, 21.913). This means that we can be 99% confident that the true mean highway mileage for SUVs falls within this range.
Step-by-step explanation:
To compute a 99% confidence interval estimate for the mean highway mileage for SUVs based on the sample data x = 19.4 mpg and s = 6.2 mpg, we can use the formula:
CI = x ± z * (s/√n)
Where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level. For a 99% confidence level, the z-score is approximately 2.576. Plugging in the values, we get:
CI = 19.4 ± 2.576 * (6.2/√97)
Computing this interval gives us:
CI = (16.887, 21.913)
This means that we can be 99% confident that the true mean highway mileage for SUVs falls within this range.
completed 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 97 SUV was selected, and the owners asked to report their highway mileage. The results that were summarized from the sample data were x = 19.4 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 is mpg mpg. Interpret this interval. Choose the correct answer below. There is a 0.99 probability that the true mean highway mpg for SUVs falls in this range. One can conclude with 99% confidence that the true mean highway mpg for SUVs is in this range. One can conclude that the true mean highway mpg for SUVs will fall in this 99% of the time. One can conclude with 99% confidence that the sample mean highway mpg for SUVS is in this range.