8.4. Population Proportion

Let be the random variable with possible values and is the population proportion.

Also, assume the sample size is large ().

Derivation of confidence interval:

Since . Thus,

.

Then,

confidence interval:

Suppose the sample size is large. By estimating by and thus estimating

by , a confidence interval for is

Example 4:

A survey conducted by Ferrell Calvillo Communications indicated 397 of 902 women golfers

were satisfied with the availability of tee times. Please construct a 95% confidence interval

for the proportion of the population of the women golfers being satisfied with availability of

tee times?

[solution:]

Determining the sample size:

Let the desired margin of error be

.

Thus,

.

can be estimated by

1. Using the sample proportion from a previous sample.

2. Using “judgment” or a “best guess” for the value

3. Use

Example 4 (continue):

In the above example, how large should the sample be if we want to obtain a margin of error

of 0.025 at a 95% confidence level in a new survey?

[solution:]

By estimating by the sample proportion in the previous survey, thus,

Therefore, a sample of 1515 women golfers is recommended!!

JavaStatSoft:

Confidence interval:

Statistics -> Estimation -> One Sample -> Proportion and Count