Question

A manufacturer claims their car gets 35 miles to the gallon. A consumer reporting agency is doubtful it is that good, they want to test the claim. A sample of 50 such cars are tested on the road and their mean miles per gallon is determined to be 33, while their variance is 64. What is the decision at the 7

Answer 1

The problem is an example of hypothesis testing where the null hypothesis is that a car achieves 35 mpg, which is tested against actual sample data with a known variance. A z-score is calculated and compared to the significance level to make a decision on the manufacturer’s claim.

Step-by-step explanation:

The question pertains to hypothesis testing in statistics, involving a consumer reporting agency that is skeptical of a manufacturer’s claim about the fuel efficiency of their car. The proper test for this scenario is a one-sample z-test, since the sample size is large (n > 30), and the variance is known.

To conduct the hypothesis test, the null hypothesis (H0) is that the true mean fuel efficiency is 35 miles per gallon, and the alternative hypothesis (H1) is that the true mean is less than 35 miles per gallon. Using the sample mean of 33 mpg, the known variance (64), and the sample size of 50 cars, one can calculate the z-score. After finding the z-score, the corresponding p-value can be looked up in a standard normal distribution table. If the p-value is less than the significance level (which appears to be cut off in the question, but we can assume a common level like 0.05, or 5%), then the null hypothesis would be rejected, suggesting the cars do not meet the manufacturer’s claim of 35 mpg.