Question

1. 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 7.9 pounds/square inch. The valve was tested on 24 engines and the mean pressure was 8.1 pounds/square inch with a variance of 0.25. Is there evidence at the 0.1 level that the valve performs above the specifications? Assume the population distribution is approximately normal.

-State the null and alternative hypotheses.

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

-Specify if the test is one-tailed or two-tailed.

-Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

-Make the decision to reject or fail to reject the null hypothesis.

2.

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 13 doors is made, and it is found that they have a mean of 2043 millimeters with a variance of 1024. Is there evidence at the 0.0250.025 level that the doors are too short and unusable?

State the null and alternative hypotheses for the above scenario.

Answer 1

Answer 1:

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ ≤ 7.9

Ha: μ > 7.9

Test Statistics

The t-statistic is computed as follows:

The test is one tailed (right) because hypothesis is directional. In other words, the researcher wants to test the claim that whether valve performs above the specifications.

Decision rule

Based on the information provided, the significance level is α=0.1 and df = 24-1 = 23

The critical value for a right-tailed test is t_c​=1.319 (Obtained using T-value calculator for α=0.1 & df = 23)

The rejection region for this right-tailed test is R = t: t > 1.319

Decision about the null hypothesis

In this case,  it is observed that t = 1.96 > t_c ​= 1.319, it is then concluded that the null hypothesis is rejected.

Conclusion

Therefore, there is enough evidence to claim that the valve performs above the specifications, at the 0.1 significance level.

***Dear Student, We can answer one question per post. Please post remaining question separately***