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= | 7.600 |
sample size n= | 290.00 |
std deviation σ= | 1.000 |
std error ='σx=σ/√n= | 0.0587 |
test stat z = '(x̄-μ)*√n/σ= | -1.70 |
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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