In 2007,13,000 internet users were surveyed and asked about their willingness to pay fees for access to websites.Of these,2,938 were definitely not willing to pay such fees.How large a sample is necessary to estimate the proportion of interest to within 2% in a 95% confidence interval?
A)18
B)307
C)1680
D)2000
E)2965

Question

Quizplus · Accepted Answer

To calculate the sample size, we use the formula:

n = p(1-p)(z/ε)^2

where:
n = sample size
p = proportion of interest (unknown)
z = z-value for the desired confidence level (95% confidence level corresponds to z=1.96)
ε = margin of error (2% = 0.02)

We know from the given information that:
p-hat (proportion of internet users who are definitely not willing to pay fees) = 2,938/13,000 = 0.225
p = 1-p-hat = 0.775

Substituting these values into the formula, we have:

n = 0.775(1-0.775)(1.96/0.02)^2 ≈ 1679.41

Rounding up, we get a sample size of 1680. Therefore, the best choice is C)1680.

In 2007,13,000 Internet Users Were Surveyed and Asked About Their