Question

combined estimate, which represents a combination of city driving (55%) and highway driving (45%). 2. If the car rental company wants to estimate the mean combined fuel economy at 95% confidence with a margin of error of no more than 0.25 mpg, how large a sample would they need? Use a t* value rounded to three decimal places and the sample information above to calculate your answer. Your answer should be an integer value. n= constructing this interval and indicate whether each of the statements below is or is not an appropriate interpretation of this confidence interval. a. We can be confident that 90% of Chevy Equinoxes have a combined fuel economy between (29.24,30.96).

Answer 1

The question involves inferential statistics, specifically hypothesis testing and sample size calculation for estimating mean fuel economy. It includes concepts like z-test, t-test, margin of error, and the central limit theorem.

Step-by-step explanation:

This question relates to inferential statistics, specifically hypothesis testing and the calculation of sample sizes for estimating parameters like the mean fuel economy. In hypothesis testing, we generally use the z-test or t-test to determine if the observed sample mean is significantly different from the hypothesized population mean. When the population standard deviation is unknown and the sample size is small, we use the t-test. To calculate the required sample size for a given margin of error, confidence level, and standard deviation, we use the formula derived from the central limit theorem:

n = (t*σ/E)^2

Where 'n' is the sample size, 't*' is the t-value associated with the desired confidence level, 'σ' is the population standard deviation (or an estimate from a similar population), and 'E' is the desired margin of error.

For the fuel economy standards study, we would perform a t-test using the provided sample mean, standard deviation, and sample size to determine if we can claim with 95% confidence that the fleet meets the new fuel economy standards. However, without a specific value for the t*, we cannot provide the exact sample size needed for a certain margin of error, but the approach described applies. Additionally, for evaluating the claims of manufacturers about nonhybrid versus hybrid sedans, again a hypothesis test is conducted, comparing two means using known population standard deviations, which indicates a z-test might be appropriate.

In conclusion, hypothesis testing and sample size calculations are crucial concepts in statistics used to make inferences about population parameters based on sample data.