Weight of Samples in Each Stratum of Population

[DragonPetter]

Homework Statement

There are three stratums of a total population of 21,000 people, one consists of 13,000 people, one of 6,000 people, and one of 2,000 people. A sample of 100 people are taken from each stratum. What is each sample member's weight?

Homework Equations

The Attempt at a Solution

let the smallest stratum have a weight of 1, then the next smallest will have a weight of 6,000/2,000 = 3, and the largest stratum will have a weight of 13,000/2,000 = 6.5


Is this the correct concept for finding the weights of each sample member?

 

[EnumaElish]

What is the goal here? Are you asked to calculate a separate average for each sample (100 people), then calculate their weighted sum?

Or are you going to calculate a pooled average (the average of 300 people)?

 

[DragonPetter]

Here let me give the full problem.

Suppose that a particular university has 6204 resident students, 13304 nonresident students, and 2401 staff, for a total population of 21909. The university president decides to obtain a stratified sample, with a total sample size of 300.

Suppose that the president decides to select a sample of 100 from each sampling stratum (instead of a self-weighted sample), for a total sample size of 300.

A. What is each sample member's weight?
B. Suppose that among the sample member, 2 resident student, 10 nonresident student, and 5 staff members expressed the opinion that campus security was bad. Use the sample results to estimate the total number of people in the population, and the total number of people within each stratum, who felt that campus security was bad.

 

[DragonPetter]

A. my answers would be (13304/2401) for nonresidents (NR), (6204/2401) for residents (R), and (2401/2401) for staffed (S) for the weights.

B. I would take these weights and multiple them by the given members of each stratum. so 2*(6204/2401) for R, 10*(13304/2401) for NR, and 5*(2401/2401) for S. Then I would add these up to get 65.578 and divide this sum by the total which is 300. I would then multiply this ratio (65.578/300) times the true total population of 21909, which would give me the total number of people in the population who expressed the opinion. Then I would use the individual weighted totals out of 300 and multiply those by the true total population of 21909 to get each stratum's population who expressed the opinion.

 

[EnumaElish]

For part (3) I would have calculated a percentage mean of 2% for sample 1, 10% for sample 2, and 5% for sample 3. Then the overall percentage mean will be:

(6204* 2% + 13304 * 10% + 2401 * 5%)/21909

I would have applied the resulting overall percentage mean to the total number of people (21909).

This should give you an idea about the weights I'd be using.

And for each stratum, I'd have applied the respective percentage mean for that stratum sample to the total number of people in the stratum (e.g. 2% x 6204 = ___).