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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 4.6 pounds/square inch (psi). Assume the population variance is 0.64. The engineer designed the valve such that it would produce a mean pressure of 4.7 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.1 will be used. Make the decision to reject or fail to reject the null hypothesis.

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Answer:

we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7 psi

Step-by-step explanation:

Let's first define the hypothesis;

Null hypothesis: H0: μ = 4.7

Alternative hypothesis: Ha: μ ≠ 4.7

We have;

Sample size; n = 110

Sample mean; x¯ = 4.6

Variance: σ² = 0.64

Standard deviation; σ = √0.64 = 0.8

Formula for test statistic is;

z = (x¯ - μ)/(σ/√n)

z = (4.6 - 4.7)/(0.8/√110)

z = -0.1/0.0763

z = -1.31

From online p-value from z-score calculator attached, using; z = -1.31, two tailed hypothesis, significance value of 0.1, we have;

P-value = 0.190196

The p-value is greater than the significance value and thus we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7

σ μ

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