Question

STATISTICS

9. Use the given information to find the minimum sample size required to estimate an unknown population proportion, p.


A recent study reported that 70% of adults go to the doctor for their yearly check up. If you want to test the validity of this claim, how many adults must be surveyed in order to be 90% confident that the sample percentage is in error by no more than five percentage points?

A. 17

B. 138

C. 228

D. 457

Answer 1

To find the minimum sample size required to estimate an unknown population proportion, we can use the formula for sample size calculation for estimating proportions. The formula is given by:

n = (Z^2 * p * (1 - p)) / E^2

where:

n is the minimum sample size required,

Z is the Z-score corresponding to the desired level of confidence (in this case, 90% confidence),

p is the estimated proportion from the previous study (70%),

E is the desired margin of error (5 percentage points or 0.05).

Substituting the values into the formula:

n = (Z^2 * p * (1 - p)) / E^2

n = (1.645^2 * 0.70 * (1 - 0.70)) / (0.05^2)

n ≈ 457.336

Rounding up to the nearest whole number, the minimum sample size required is 457.

Therefore, the answer is D. 457.

Explanation: