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medical researcher wishes to determine the percentage of females who take vita to be 99% confident that the estimate is within 2 percentage points of th survey showed that 25% of females took vitamins. How large should a sample size be? 3 A A medical researcher wishes to determine the percentage of females who take vitamins. He wishes e true proportion. A recent a) b) If no estimate of the sample proportion is available, how large should the sample be?
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Answer #1

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(A) We have proportion p = 25% = 25/100 = 0.25

margin of error=ME= 2% = 2/100 = 0.02

For 99% confidence level, z score = 2.58 (using z distribution table)

we have to find the sample size n

formula for sample size n is given as

n = (p*(1-p))*(z/ME)^2

setting the given values, we get

n = (0.25 * (1-0.25)) * (2.58/0.02)2-0.1875 * 16641 = 3120.1875

rounding it off to next whole number, we get

sample size n = 3121

(b) When we have no prior estimate for proportion, we have to use the following formula

sample size n = 0.25 * (z/ME)2

setting z = 2.58 and ME=0.02

we get, n = 0.25 * (2.58/0.02)2 = 0.25 * 16641 = 4160.25

rounding it off to next whole number, we get

sample size n = 4161

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