Question

A manufacturer claims that a particular automobile model will get 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine believe that this claim is high and plan a test with a simple random sample of 25 cars. What should the researchers conclude if the sample mean is 49 miles per gallon with standard deviation 2.3 miles per gallon

Answer 1

Following are the responses to the given question:

Explanation:

Given values:

`The \ population\ mean(\bar{x})=50\\\\The \ sample \ mean, \mu =49\\\\standard \ deviation, \sigma =2.3\\\\ (n)=25\\\\null, H_o :\ \mu=50\\\\alternate, H_1 :\ \mu<50\\\\ testing \ the \ statistic (t) = \frac{\bar{x}-\mu}{(\sigma)/(\sqrt(n))}\\\\to = (49-50)/((2.3)/(√(25)))\\\\to =-2.1739\\\\| to | =2.1739\\\\p-value\ :left \ tail - H_a : (p < -2.1739 )=0.0199\\\\null, H_o: \ \mu=50\\\\alternate, H_1: \ \mu<50\\\\test \ statistic: \ -2.1739\\\\p-value: 0.0199 \sim 0.02\\\\`

Therefore, the 0.02 p-value is sufficient proof to reject the claim form of the manufacturer.