Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 180 engines and the mean pressure was 5.7 pounds/square inch (psi). Assume the population standard deviation is 0.8. lf the valve was designed to produce a mean pressure of 5.6 psi, is there sufficient evidence at the 0.1 level that the valve performs above the specifications? Step 1 of 6: State the null and alternative hypotheses. Answer 1 Point Keypad Hide H

Answer 1

Given that, sample size (n) = 180

sample mean $(\bar x)$ = 5.7 psi and

population standard deviation $(\sigma)$ = 0.8

Step 1) The null and alternative hypotheses are,

H0 : μ = 5.6

Ha : μ > 5.6

Step 2) Test statistic is,

–μ 5.7 – 5.6 0.8 -=1.68 V180

=> Test statistic is, Z = 1.68

Step 3) This test is one-tailed test.

Step 4) p-value = P(Z > 1.68)=1-P(Z<1.68) =1 - 0.9535 = 0.0465

=> p-value = 0.0465

Step 5) level of significance $(\alpha)$ = 0.1

Step 6) Since, p-value < 0.1, we Reject Null Hypothesis.

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