Ask Question
24 April, 12:27

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.

+3
Answers (1)
  1. 24 April, 16:02
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “The developer of an energy-efficient lawn mower engine claims that the engine will run continuously for 300 minutes on a single gallon of ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers