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 6.16.1 pounds/square inch. The valve was tested on 190190 engines and the mean pressure was 6.06.0 pounds/square inch. Assume the standard deviation is known to be 0.80.8. Is there evidence at the 0.050.05 level that the valve performs below the specifications?

Step 1 of 5:

Enter the hypotheses:

enter value of the z test statistic

specify one tailed or two tailed

enter decision rule

enter the conclusion

Answer 1

n = 190

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.

Now, the value of test static can be found out by following formula:

Using Excel's function =T.DIST.2T(|t0|,n-1), the P-value for t0 = -1.723 in an t-test with 189 degrees of freedom can be computed as

Since P = 0.0865 > 0.05, we fail to reject the null hypothesis

Since t0 = -1.723 < -1.97 = -t{0.025}, we fail to reject the null hypothesis