Question

Note that the proportion of students who went Home for winter break was 0.35 (or 35%). Briefly explain why it would not be appropriate to refer to the 0.35 proportion as a parameter

Answer 1

Is not appropiate to refer a estimation or a statistic as a paramter because the statistic just give informaation about the sample selected and not about all the population of interest. What we can do is inference with this sample proportion or confidence intervals in order to see on what limits our real parameter of interest p lies.

Explanation:

Description in words of the parameter p

`p` represent the real population proportion of students who went Home for winter break

`\hat p` represent the estimated proportion of students who went Home for winter break

n is the sample size selected

The population proportion have the following distribution

`p \sim N(p,\sqrt{(p(1-p))/(n)})`

Solution to the problem

For this case we assume that the proportion given 0.35 is an estimation for the real parameter of interest p, that means
`\hat p = 0.35`

On this case the estimated proportion is calculated from the following formula:

`\hat p = (X)/(n)`

Where X are the people in the sam with the characteristic desired (students who went Home for winter break) and n the sample size selected.

Is not appropiate to refer a estimation or a statistic as a paramter because the statistic just give informaation about the sample selected and not about all the population of interest. What we can do is inference with this sample proportion or confidence intervals in order to see on what limits our real parameter of interest p lies.