Question

Suppose you are thinking of contracting with Company A to supply a certain component to your manufacturing facility. As part of your quality control regimen, you purchase a small sample and run some tests. Suppose you find the mass of 10 of these components to be 10.1, 12.0, 9.7, 10.0, 9.9, 9.2, 10.1, 11.2, 9.4, and 10.0. What is the population in this scenario? What is the sample? What is population mean, and what is population variance? (you won’t be f

Answer 1

- The population is the group of all the components that will be supplied by the Company A.

- The sample is the group of 10 components that were selected to be evaluted.

- These values can not be known, but estimated by the sample values.

Population mean: 10.16

Population variance: 0.78

Explanation:

What is the population in this scenario?

In this case, the population is represented by all the components that will be supplied by the Company A.

What is the sample?

The sample is the group of 10 components that were selected to be evaluted. They are a subgroup of the population, that is thinked to be representative of it.

What is population mean, and what is population variance?

These values can not be known, but estimated by the sample values.

In the case of the population mean can be estimated by the sample mean, that is M=10.16.

`M=(1)/(10)\sum_(i=1)^(10)(10.1+12+9.7+10+9.9+9.2+10.1+11.2+9.4+10)\\\\\\ M=(101.6)/(10)=10.16`

Then, we can estimate the population mean as μ≈M=10.16.

The population variance can be estimated from the sample variance, but with correction factor, taking into account the sample size.

The sample variance is 0.7, so the estimated population variance is:

`\sigma^2=(n)/(n-1)s^2=(10)/(9)\cdot 0.7=0.78`