Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 220 engines and the mean pressure was 5.4 pounds/square inch (psi). Assume the population standard deviation is 0.6 . If the valve was designed to produce a mean pressure of 5.5 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications?

Step 1 of 6: State the null and alternative hypotheses.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that,

Step 1 of 6:

The null and alternative hypothesis is,

Ho: 5.5

Ha: 5.5

Step 3 of 6:

This is a two tailed test.

Step 4 of 6

The test statistics,

Z =( - )/ (/n)

= ( 5.4 - 5.5 ) / ( 0.6 / 220 )

= -2.47

P-value = 2 * P(Z < -2.47 )

= 2 * 0.0068

= 0.0136

Step 5 of 6:

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 1.96

Step 6 of 6:

The p-value is p = 0.0136, and since p = 0.0136 < 0.05, it is concluded that the null hypothesis is rejected.