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If n=370 and p (p-hat) =0.18, find the margin of error at a 95% confidence level Give your answer to three decimals

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Final answer:

To compute the margin of error at a 95% confidence level with n=370 and p=0.18, you use the formula involving the z-score of 1.96; the resulting margin of error is approximately 0.039 when rounded to three decimal places.

Step-by-step explanation:

The margin of error for a proportion at a specified confidence level can be found using the formula √[p(1-p)/n]*z, where p (or p-hat) is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level. To find the margin of error at a 95% confidence level when n=370 and p=0.18, we first need the z-score for 95% confidence, which is typically 1.96 (found in z-tables or using statistical software/calculators). Then, using the formula, the margin of error (ME) is calculated as follows:

ME = √[(0.18)(1-0.18)/370]*1.96
ME = √[(0.18)(0.82)/370]*1.96
ME = √(0.1476/370)*1.96
ME = √(0.000399)*1.96
ME = 0.01996*1.96
ME ≈ 0.039

Thus, the margin of error at a 95% confidence level, rounded to three decimal places, is approximately 0.039.

User Md Shopon
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