A researcher conducts a study to determine what the population proportion is for a given characteristic.It is believed from previous studies that the proportion of the population will be at least .65.The researcher wants to use a 98% level of confidence.He also wants the error to be no more than .03.The sample size should be at least ___.
A)41
B)313
C)1677
D)1373
E)1500

Question

Quizplus · Accepted Answer

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

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

where: 
z = the z-score for the level of confidence (in this case, 2.33 for a 98% level of confidence) 
p = the estimated population proportion (.65) 
E = the maximum allowable error (.03)

Plugging in these values, we get:

n = (2.33^2 * .65 * .35)/.03^2 = 1372.97

Since we need a whole number for the sample size, we round up to the nearest integer, which is 1373. Therefore, the best choice is D.

A Researcher Conducts a Study to Determine What the Population