Question

# An engineer has designed a valve that will regulate water pressure on an automobile engine. The...

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 7.6 pounds/square inch (psi). Assume the population standard deviation is 1.0. If the valve was designed to produce a mean pressure of 7.7 psi, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Step 1 of 6:

 null hypothesis:Ho μ = 7.7 Alternate Hypothesis:Ha μ ≠ 7.7

Step 2 of 6:

 population mean μ= 7.7 sample mean 'x̄= 7.6 sample size    n= 290 std deviation σ= 1 std error ='σx=σ/√n= 0.0587 test stat z = '(x̄-μ)*√n/σ= -1.7

Step 3 of 6:

two-tailed.

Step 4 of 6:

 p value        = 0.0892

Step 5 of 6:

level of significance for the hypothesis test =0.02

Step 6 of 6:

fail to reject the null hypothesis.

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