Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 6.4 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario. Null: mean equals 6.5 Alt: mean does not equal 6.5

Answer 1

The null and alternate hypothesis are:
H0:
Ha:

The test statistic is given by:

Since this is a two-tailed test, so the p-value is given by:

Since p-value is greater than 0.05, so we do not have sufficient evidence to reject the null hypothesis
H0. So, we do not reject H0 and we can say that the valve produces a mean pressure of 6.5 lbs/square inch.