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.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.