Question

An engineer 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 6.8 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 6.9 pounds/square inch with a variance of 1.00. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

Solution:

From given claim , we write the null and alternative hypothesis

H0: = 6.8

H1: > 6.8

Right tailed test

Given ,

n = 24 ....sample size

= 6.9 ...sample mean

s² = 1 ....Sample standard deviation

= 0.05 .... level of significance

Determine the decision rule for rejecting the null hypothesis.

Degrees of freedom df = n - 1 = 24 - 1 = 23

Right tailed test (Because > sign in H1)

So, the critical value is  

= = 1.714

Decision Rule : Reject H₀ if t > 1.714