Final answer:
. The correct answer is option BTo estimate the sample size needed, the researcher can use the formula: n = (Z * p * (1-p)) / E^2, where n is the sample size, Z is the z-score for the desired confidence level, p is the estimated proportion, and E is the maximum margin of error. In this case, the researcher wants to be 95% sure that the obtained sample proportion would be within 2.4% of p. Therefore, the correct sample size is 1737.
Step-by-step explanation:
To estimate the sample size needed, we need to use the formula:
n = (Z * p * (1-p)) / E^2
where:
- n is the sample size
- Z is the z-score for the desired confidence level
- p is the estimated proportion
- E is the maximum margin of error
In this case, the researcher wants to be 95% sure that the obtained sample proportion would be within 2.4% of p. Since the range around p is 2.4%, the margin of error (E) is 2.4% / 2 = 1.2% = 0.012. The Z-score for a 95% confidence level is approximately 1.96.
Substituting these values into the formula:
n = (1.96^2 * p * (1-p)) / 0.012^2
Since we don't have an estimated proportion, we can assume a worst-case scenario of p = 0.5 (maximum variability). Plugging in this value:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.012^2 = 1693.44
Rounding up to the nearest whole number, the sample size should be 1694. Therefore, the correct option is B. 1,737.