Question

The population proportion is .65 . What is the probability that a sample proportion will be within + or - .02 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table. a. n=100 b. n=200 c. n=500 d. n=1000 e. What is the advantage of a larger sample size? With a larger sample, there is a probability will be within + or - .02 of the population proportion .

Answer 1

(a)

Here we have

p = 0.65, n=100

Here we have

The z-score for is

The z-score for is

So the probability that a sample proportion will be within +/-0.02 of the population proportion for each of the following sample sizes is

(b)

Here we have

p = 0.65, n=100

Here we have

The z-score for is

The z-score for is

So the probability that a sample proportion will be within +/-0.02 of the population proportion for each of the following sample sizes is

(c)

Here we have

p=0.65, n=500

Here we have

The z-score for is

The z-score for is

So the probability that a sample proportion will be within +/-0.02 of the population proportion for each of the following sample sizes is

(d)

Here we have

p=0.65, n=1000

Here we have

The z-score for is

The z-score for is

So the probability that a sample proportion will be within +/-0.02 of the population proportion for each of the following sample sizes is

(e)

higher