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 4.4 pounds/square inch. The valve was tested on 120engines and the mean pressure was 4.6 pounds/square inch. Assume the standard deviation is known to be 0.8 Is there evidence at the 0.01 level that the valve performs above the specifications?
Step 1 of 5: Enter the hypotheses:
Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places.
Step 3 of 5: Specify if the test is one-tailed or two-tailed.
Step 4 of 5: Enter the decision rule.
Reject H0 if Z>
Step 5 of 5: Enter the conclusion. Reject Null Hypothesis or Fail to Reject
Step 1: Here claim is that mean is greater than 4.4
As null hypothesis always have equality sign, so hypothesis is vs
Step 2: Here
Hence test statistics is
Step 3: Here alternative hypothesis have greater than sign so it is one tailed test.
Step 4: The z-critical value for a right-tailed test, for a significance level of α=0.01 is
zc=2.33
Graphically
So decision rule is
Reject H0 if Z>2.33
Step 5: As we see that ztest=2.74>zcal=2.33
We reject the null hypothesis
Hence we have sufficient evidence to support the claim that mean is greater than 4.4
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