Ask Question
25 May, 23:56

g An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 4.8 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 4.9 psi, is there sufficient evidence at the 0.1 level that the valve performs below the specifications

+2
Answers (1)
  1. 26 May, 00:22
    0
    Step-by-step explanation:

    We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

    For the null hypothesis,

    µ = 4.9

    For the alternative hypothesis,

    µ < 4.9

    This is a left tailed test.

    If the population variance is 0.36, the population standard deviation would be √0.36 = 0.6 psi

    Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

    z = (x - µ) / (σ/√n)

    Where

    x = sample mean

    µ = population mean

    σ = population standard deviation

    n = number of samples

    From the information given,

    µ = 4.9

    x = 4.8

    σ = 0.6

    n = 210

    z = (4.8 - 4.9) / (0.6/√210) = - 2.42

    Looking at the normal distribution table, the probability corresponding to the z score is 0.0078

    Since alpha, 0.1 > than the p value, 0.0078, then we would reject the null hypothesis. Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “g An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers