Question

A car manufacturer claims that the company's newest model has a peak power of exactly 329 horsepower. Katherine is a reporter for an automotive magazine. She is testing the manufacturer's claim and says that the population mean peak power is less than the advertised amount. She measures the peak horsepower of 42 randomly selected cars of the new model. The sample mean is 327.74 horsepower with a standard deviation of 2.41 horsepower. Should Katherine reject or fail to reject the null hypothesis given the sample data below?• H = 329 versus H: < 329 • a=0.05 (significance level) .te-3.39 with 41 degrees of freedom . p-value< 0.005Select the correct answer below: A. Reject the null hypothesis because p-value < 0.005 is less than the significance level a = 0.05. B. Reject the null hypothesis because -3.39 <0.05. C. Fail to reject the null hypothesis because p-value < 0.005 is less than the significance level a 0,05

Answer 1

A. Reject the null hypothesis because p-value < 0.005 is less than the significance level a = 0.05

Explanation:

In hypothesis test, test statistic calculated and it's p-value is compared against the significance level. If it is less than the significance level, the result is significant at the given significance level. In this case one can reject the null hypothesis in favor of the alternate hypothesis.

In this example Katherine find test statistic -3.39, and p-value < 0.005. Thus she can conclude there is significant evidence that the population mean peak power is less than the advertised amount