Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 6.5 pounds/square inch (psi). Assume the population variance is 1.00. If the valve was designed to produce a mean pressure of 6.4 psi, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications? Step 1 of 6 : State the null and alternative hypotheses.

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290290 engines and the mean pressure was 6.56.5 pounds/square inch (psi). Assume the population variance is 1.001.00. If the valve was designed to produce a mean pressure of 6.46.4 psi, is there sufficient evidence at the 0.10.1 level that the valve does not perform to the specifications?

Step 2 of 6 :  

Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Solution:

Step 1)

The null and alternative hypothesis are

H₀: = 6.4

H_a ;    6.4

Step 2)

Given , ² = 1.00

So that , = 1.00

The test statistic z is given by

z =

= (6.5 - 6.4) / (1.00/290)

= 1.70

Test statistic z = 1.70