Question

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 6.6 pounds/square inch. The valve was tested on 120 engines and the mean pressure was 6.8 pounds/square inch. Assume the variance is known to be 1.00. Is there evidence at the 0.05 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.

Step 5 of 5: Enter the conclusion. Reject or Fail to Reject?

Answer 1

Step 1 )

H0: = 6.6

Ha: > 6.6

Step 2)

Test statistics

z = - / ( / sqrt(n) )

= 6.8 - 6.6 / 1 / sqrt(120) )

= 2.19

Step 3)

This is one tailed test.

Step 4)

From Z table,

z critical value at 0.05 significance level is 1.645

Decision rule = Reject H0 if test statistics z > 1.645

Step 5)

Since test statistics falls in rejection region, Reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.