Question

An engineer has 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 5.7 pounds/square inch. The valve was tested on 13 engines and the mean pressure was 5.5 pounds/square inch with a standard deviation of 0.7 . Is there evidence at the 0.01 level that the valve performs below the specifications? Assume the population distribution is approximately normal.

Step 1 of 5 : State the null and alternative hypotheses

Step 2: enter the value of the z test statistic rounded to two decimals

Step 3: critical value

Step 4: specify if its one or two tailed

Step 5: enter the decision rule

Step 6: enter the conclusion

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 5.7

Ha : < 5.7

Test statistic (t) =

= ( - ) / s / n

= (5.5 - 5.7) / 0.7 / 13

Test statistic = -1.03

P-value = 0.1616

= 0.01

P-value >

Fail to reject the null hypothesis .

There is insufficient evidence at the 0.01 level that the valve performs below the specifications