Question

Suppose you are looking at the population of 8,000 students that are freshman at UTEP. You want to determine on average how many hours a week they work each week. Let’s call that number ?. You decide to take a sample of 100 of them.

1) How many data points are there in this space?

2) How many ways can you choose your subest of 100 students? Is it greater or less than the answer above.

3) How do you calculate the “point estimate” of one of those subsets of 100 students?

4) How many actual subsets of 100 students do you have as a researcher?

5) What does the Central Limit Theorem say about all the possible point estimates that can occur from the possible 100-student subsets? Draw a graph.

6) What value is the center of that curve? Please label it on the graph above.

Answer 1

Answer:

Given that,

Suppose you are looking at the population of 8,000 students that are freshman at UTEP.

You want to determine on average how many hours a week they work each week.

Let’s call that number ?. You decide to take a sample of 100 of them.

(1).

How many data points are there in this space:

There are 8000 data points in this space , for each of the 8000 students hours/work spend working.

(2).

How many ways can you choose your subest of 100 students? Is it greater or less than the answer above:

We can choose subset of 100 students in ways,

=

=1.17 10232 Ways.

(3).

How do you calculate the “point estimate” of one of those subsets of 100 students:

We conclude the point estimate as one of these subsets of 100 students by calculating the sample mean of hours/week spend working by each of the 100 students in the sample.

i=i(1)=100

Where,hi=hours/week spend working by ith student of the sample.

(4).

How many actual subsets of 100 students do you have as a researcher:

We have 1 subset of 100 students.

(5).

What does the Central Limit Theorem say about all the possible point estimates that can occur from the possible 100-student subsets? Draw a graph:

CLT states that for large sample size, irrespecctive of popl "dist".

(6).

What value is the center of that curve? Please label it on the graph above:

Center of the curve has value i.e, .