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14 July, 04:45

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

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  1. 14 July, 07:21
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    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.
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