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An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 7.3 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

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Answer:

Step-by-step explanation:

Given that:

Population Mean = 7.1

sample size = 24

Sample mean = 7.3

Standard deviation = 1.0

Level of significance = 0.025

The null hypothesis:

[tex]H_o: \mu = 7.1[/tex]

The alternative hypothesis:

[tex]H_a: \mu > 7.1[/tex]

This test is right-tailed.

[tex]degree \ of \ freedom= n - 1 \\ \\ degree \ of \ freedom = 24 - 1 \\ \\ degree \ of \ freedom = 23[/tex]

Rejection region: at ∝ = 0.025 and df of 23, the critical value of the right-tailed test [tex]t_c = 2.069[/tex]

The test statistics can be computed as:

[tex]t = \dfrac{ \hat X - \mu_o}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t = \dfrac{ 7.3-7.1}{\dfrac{1}{\sqrt{24}}}[/tex]

[tex]t = \dfrac{0.2}{0.204}[/tex]

t = 0.980

Decision rule:

Since the calculated value of t is lesser than, i.e t = 0.980 < [tex]t_c = 2.069[/tex], then we do not reject the null hypothesis.

Conclusion:

We conclude that there is insufficient evidence to claim that the population mean is greater than 7.1 at 0.025 level of significance.

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