Question

Test run with 6 models of an experimental engine showed that they operated for 24, 28, 21, 23, 32, and 22 minutes with a gallon of a certain kind of fuel and is normally distributed. If the probability of type I error is 0.01, is this evidence against a hypothesis that on average this kind of engine will operate for at least 29 minutes per gallon with this kind of fuel?

Answer 1

The hypothesis test fails to reject the claim that the average operating time of the experimental engine is at least 29 minutes per gallon.

Step-by-step explanation:

To conduct the hypothesis test, we can use a one-sample t-test since we don't know the standard deviation of the population. The null hypothesis (H0) is that the average operating time of the engine is at least 29 minutes per gallon. The alternative hypothesis (Ha) is that the average operating time is less than 29 minutes per gallon.

To perform the hypothesis test, we calculate the t-statistic using the sample mean, sample standard deviation, sample size, and hypothesized population mean. We find that the t-statistic is approximately -2.400. With a significance level of 0.01, the critical t-value is -2.626.

Since the t-statistic is greater than the critical t-value, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the average operating time of the engine is less than 29 minutes per gallon.