A soap manufacturer wants to know within +4 percentage points what percentage of households use liquid soaps.To be 95% confident in the estimate,how many households should be sampled? (Note: a confidence interval greater than +4 percentage points is unacceptable. )
A)600
B)625
C)700
D)750
E)550

Question

Quizplus · Accepted Answer

The formula to find the sample size needed to estimate the population proportion with a certain level of confidence and margin of error is:

n = (Z^2 * p * q) / E^2

Where:
- Z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case, which corresponds to Z = 1.96)
- p is the estimated proportion of households that use liquid soaps (unknown, but we can assume a value of 0.5 for a conservative estimate)
- q is the complementary probability of p (q = 1 - p)
- E is the maximum margin of error (+/-4 percentage points, or 0.04)

Plugging in the values:

n = (1.96^2 * 0.5 * 0.5) / 0.04^2
n = 600.25

Rounding up to the nearest integer, we get:

n = 625

Therefore, the best choice is B) 625 households.

A Soap Manufacturer Wants to Know Within +4 Percentage Points