Feb 27th - Stony Brook University
Feb 27th
Sample size determination:
1) In the scenario of estimating a population mean;
2) In the scenario of estimating a population proportion.
1.Sample size determination for the estimation of one population proportion based on the margin of error (or maximum error, or the length of the confidence interval).
Example 1: (P374 example 5.3.4)
A public health survey is being planned in a large metropolitan area for the purpose of estimating the proportion of children, ages zero to fourteen, who are lacking adequate polio immunization. Organizers of the project would like the sample proportion of inadequately immunized children, [pic], to have at least a 98% probability of being within 0.05 of the true proportion, p. How large should the sample be?
[pic]
0.05: E: maximum error (or margin of error)
0.98: [pic]
Derivation of the general formula:
[pic]
[pic]
Let[pic], since[pic],
we have:
[pic]
Thus,
[pic] Hence, [pic], that is:
[pic]
Solution to the example above: Plug in E=0.05, α=0.02, we have
[pic]
Relationship between E&L, the length of the [pic] C.I. for p: L=2E
Equivalently, we can ask the question for sample size calculation in Example 1 in terms of the length of the confidence interval as: “What is the sample size necessary to guarantee that the length of the 98% C.I. for p is no more than 0.1?”
[pic]
2.Sample size determination for the estimation of one population mean based on the margin of error (or maximum error, or the length of the confidence interval).
Example 2: In order to estimate the IQ of the freshman in Trinity College. The school principal decided to draw a random sample. He wishes to estimate the average IQ within 5 points (full score being 140) with a probability of 95%.
Assuming the population is normal, we have the following relationship between range and the population standard deviation: [pic]
In Example 2, suppose from past experience we know that the range of the test is 60 and thus we estimate [pic]. Also in this problem, we have E=5, α=0.05.
Derivation of the general formula:
P.Q. [pic]
[pic]
[pic]
[pic]
Hence we can calculate the sample size needed for Example 2 is
[pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.