Question

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 140 engines and the mean pressure was 6.9 pounds/square inch (psi). Assume the population standard deviation is 0.7. The engineer designed the valve such that it would produce a mean pressure of 6.8 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 6.8 psi

For the alternative hypothesis,

µ ≠ 6.8

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 6.8

x = 6.9

σ = 0.7

n = 140

z = (6.9 - 6.8)/(0.7/√140) = 0.17

Therefore, the value of the test statistic us 0.17