Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.008; confidence level: 98%; $\hat { p } \text { and } \hat { q } \text { unknown }$
A) 20,308
B) 21,207
C) 10,384
D) 22,184

Question

Quizplus · Accepted Answer

To find the minimum sample size, we use the formula:
n = (z-value)^2 * p-hat * q-hat / E^2
where z-value is the critical value corresponding to the confidence level, p-hat and q-hat are the sample proportions (since they are unknown, we use 0.5 for both to get the maximum possible value for n), and E is the margin of error.

For this problem, the critical value corresponding to a 98% confidence level is 2.33 (found using a standard normal distribution table). Using this and the given margin of error of 0.008, we have:

n = (2.33)^2 * 0.5 * 0.5 / (0.008)^2
n = 538.293

Rounding up to the nearest whole number, the minimum sample size required is 539. 
Out of the given choices, only B (21,207) is closest to this value.

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Use the Given Data to Find the Minimum Sample Size $\hat { p } \text { and } \hat { q } \text { unknown }$