Question

The valve was tested on 250 engines and the mean pressure was 7.3 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 7.2 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 answe

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,

H0: µ = 7.2

For the alternative hypothesis,

H1: µ ≠ 7.2

This is a two tailed test.

Since the population standard deviation is given, the test statistic would be the z score 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 = 7.2

x = 7.3

σ = 0.8

n = 250

z = (7.3 - 7.2)/(0.8/√250) = 1.976

Test statistic is 1.976