A study will be conducted to estimate the population proportion.A level of confidence of 99% will be used and an error of no more than .04 is desired.There is no knowledge as to what the population proportion will be.The size of sample should be at least ___.
A)1037
B)160
C)41
D)259
E)289

Question

Quizplus · Accepted Answer

To find the minimum sample size required, we use the formula n = (z^2 * p * (1-p)) / E^2, where:
- z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for a 99% confidence level)
- p is the estimate of the population proportion (since we have no prior knowledge, we can use 0.5 to get the maximum possible sample size)
- E is the desired margin of error (0.04 in this case)

Plugging in the values, we get:
n = (2.576^2 * 0.5 * 0.5) / 0.04^2
n = 1036.9

Rounding up to the nearest integer, we get a minimum sample size of 1037. Therefore, the best choice is A).

A Study Will Be Conducted to Estimate the Population Proportion