G An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 4.8 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 4.9 psi, is there sufficient evidence at the 0.1 level that the valve performs below the specifications

Step-by-step 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 = 4.9

For the alternative hypothesis,

µ < 4.9

This is a left tailed test.

If the population variance is 0.36, the population standard deviation would be √0.36 = 0.6 psi

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 = 4.9

x = 4.8

σ = 0.6

n = 210

z = (4.8 - 4.9)/(0.6/√210) = - 2.42

Looking at the normal distribution table, the probability corresponding to the z score is 0.0078

Since alpha, 0.1 > than the p value, 0.0078, then we would reject the null hypothesis. Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications.