Question

An automobile manufacturer claims that its car has a 52.6 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this car since it is believed that the car has an incorrect manufacturer's mpg rating. after testing 180 cars, they found a mean mpg of 52.7 . assume the standard deviation is known to be 2.4 . a level of significance of 0.01 will be used. state the hypotheses. enter the hypotheses:

Answer 1

The null hypothesis (H0) is that the mean mpg rating of the cars is 52.6 mpg, and the alternative hypothesis (Ha) is that the mean mpg rating is not equal to 52.6 mpg, using a significance level of 0.01 for the test.

Step-by-step explanation:

The hypotheses for the question concerning the automobile manufacturer's claim of 52.6 miles per gallon (mpg) can be formulated as follows:

The null hypothesis states that the mean mpg rating of the cars by the manufacturer is equal to 52.6 mpg. The alternative hypothesis states that the mean mpg rating of the cars is different from the 52.6 mpg claimed by the manufacturer. A significance level of 0.01 indicates that the testing firm has a 1% threshold for accepting the risks of a Type I error, where the null hypothesis would be incorrectly rejected. It is important to note that a Type I error is a false positive, in other words, rejecting the null hypothesis when it is actually true. In testing this claim, the mean of 52.7 mpg observed from 180 cars will be compared with the population mean of 52.6 mpg, using the given population standard deviation of 2.4 mpg, to assess the validity of the manufacturer's claim using statistical methods.