A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.If the researcher would like to be 95% sure that the obtained sample proportion would be within 2.4% of p (the proportion in the entire population of U.S. adults), what sample size should be used? 6,945 1,737 435 42
Question
A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.If the researcher would like to be 95% sure that the obtained sample proportion would be within 2.4% of p (the proportion in the entire population of U.S. adults), what sample size should be used? 6,945 1,737 435 42
Solution
To answer this question, we need to use the formula for sample size in proportion:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the Z-score (for a confidence level of 95%, Z = 1.96)
- p is the estimated proportion (since we don't have a specific value, we use 0.5 for maximum variability)
- E is the margin of error (2.4% or 0.024 in decimal form)
Substituting the values into the formula:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.024^2 n = 3.8416 * 0.25 / 0.000576 n = 0.9604 / 0.000576 n = 1667.36
Since we can't have a fraction of a person, we round up to the nearest whole number. So, the researcher should use a sample size of 1,668.
However, none of the options provided (6,945, 1,737, 435, 42) match this result. The closest option is 1,737.
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