Question
A manager at a drug manufacturing wants to estimate what proportion of the adult population of India has high blood pressure. He wants to be 99% sure that the error of his estimate will not exceed 0.02. Census reports indicate that about 0.20 of all adults have high blood pressure. What sample size shall he take?
Answer :
Word Count : 881
To determine the required sample size for estimating the proportion of adults in India who have high blood pressure, we must use the sample size formula for estimating a population proportion with a specified level of confidence and margin of error. The formula is: $$ n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right) $$ Where: * $n$ = required sample size * $Z$ = Z-score corresponding to the desired confidence level * $p$ = estimated population proportion * $E$ = desired margin of error ### Step 1: Identify the known values * Confidence level = 99% * From Z-tables, the Z-value corresponding to 99% confidence level is approximately 2.576 * Estimated proportion, $p = 0.20$ (as per census reports) * Desired margin of error, $E = 0.02$ ### Step 2: Plug the values into the formula $$ n = \frac{(2.576)^2 \cdot 0.20 \cdot ____ _____ ___ _________ ______ _______.
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To determine the required sample size for estimating the proportion of adults in India who have high blood pressure, we must use the sample size formula for estimating a population proportion with a specified level of confidence and margin of error. The formula is: $$ n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right) $$ Where: * $n$ = required sample size * $Z$ = Z-score corresponding to the desired confidence level * $p$ = estimated population proportion * $E$ = desired margin of error ### Step 1: Identify the known values * Confidence level = 99% * From Z-tables, the Z-value corresponding to 99% confidence level is approximately 2.576 * Estimated proportion, $p = 0.20$ (as per census reports) * Desired margin of error, $E = 0.02$ ### Step 2: Plug the values into the formula $$ n = \frac{(2.576)^2 \cdot 0.20 \cdot ____ _____ ___ _________ ______ _______.
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