Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 6.7 pounds/square inch (psi). Assume the population variance is 0.81 . If the valve was designed to produce a mean pressure of 6.5 psi, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? Step 1 of 6 : State the null and alternative hypotheses.

Answer 1

Given that, population variance = 0.81

=> population standard deviation = √(0.81) = 0.9

sample size (n) = 160 and sample mean = 6.7 psi

The null and alternative hypotheses are,

H0 : μ = 6.5

Ha : μ > 6.5

Test statistic is,

=> Test statistic = 2.81

critical value at significance level of 0.02 is Z_{​​​​​​crit} = 2.05

=> Critical value = 2.05

Decision Rule : Reject H0, if Z > 2.05

Since, test statistic = Z = 2.81 > 2.05, we should reject H0.

Therefore, there is significant evidence at the 0.02 level that the valve performs above the specifications.

p-value = P(Z > 2.81) = 1 - P(Z < 2.81)= 1 - 0.0075 = 0.0025

=> p-value = 0.0025

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