A supplier of television programs through a satellite service is planning to offer a new package and would like to determine what proportion of the households in their region would purchase this new package.Based on past experience it is thought that it is likely 25% to 35% of households will purchase the package.If the supplier wants to be 95% confident in the outcome,how many households should they randomly sample to achieve a margin of error no greater than ± 0.025 in their estimate?
A)922
B)985
C)350
D)1399
E)Not within ± 25 of any of the above

Question

Quizplus · Accepted Answer

To calculate the sample size needed, we use the formula:

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

Where:
Z = 1.96 (for 95% confidence level)
p = 0.3 (average of 25% and 35%)
q = 0.7 (1 - p)
E = 0.025

Plugging in the values, we get:

n = (1.96^2 * 0.3 * 0.7) / 0.025^2
n = 1398.68

Rounding up, we get a sample size of 1399 households. Therefore, the best choice is D.

A Supplier of Television Programs Through a Satellite Service Is