The developer of an energy-efficient lawn mower engine claims that the engine will run continuously for 300 minutes on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tested. The engines run for an average of 295 minutes, and the population standard deviation sigma is known to be 20 minutes. Test the null hypothesis that the mean run time is 300 minutes against the alternative hypothesis that the mean run time is not 300 minutes. Use a 0.05 level of significance.

The mean run time is 300 minutes

Step-by-step explanation:

Null hypothesis: The mean run time is 300 minutes

Alternate hypothesis: The mean run time is not 300 minutes

Test statistic (z) = (sample mean - population mean) : sd/√n

sample mean = 295 minutes, population mean = 300 minutes, sd = 20 minutes, n = 50

z = (295 - 300) : 20/√50 = - 5 : 2.83 = - 1.77

The test is a two tailed test. The critical value using a significance level of 0.05 is 1.96

Since the test is two tailed, the region of no rejection of the null hypothesis lies between - 1.96 and 1.96

The test statistic (-1.77) falls within the region bounded by - 1.96 and 1.96, fail to reject the null hypothesis

Conclusion: The mean run time is 300 minutes