Question

A prior study determined the point estimate of the population proportion as 23% ( = 0.23). The analysts want to conduct a second survey about the same topic that has a margin of error, E, of 17% and a confidence level of 99% (z*-score of 2.58).

What is the minimum sample size that should be used so the estimate of will be within the required margin of error of the population proportion?

n = (1 – ) •

3
7
12
41

Answer 1

The answer is D. 41 hoped i helped

Answer 2

We have:

z-score = 2.58
Proportion, p = 0.23
q = 1 - 0.23 = 0.77
Margin of error, E = 17% = 0.17

Step 1:
Multiply
`p` by
`q` = 0.23 × 0.77 = 0.1771

Step 2:
Divide z-score by the margin error = 2.58 ÷ 0.17 = 15.2

Step 3:
Square the answer from step 2 = 15.2² = 230.32

Step 4:
Multiply the answer from Step 1 by the answer in step 3
= 0.1771 × 230.32 = 40.79

The answer is the sample size is 40.79 rounded to 41

Answer: Last Option