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In: Statistics and Probability

Based on prior studies, about 10% of Californians are left-handed. Find the minimum sample size needed...

Based on prior studies, about 10% of Californians are left-handed. Find the minimum sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of two percentage points, and use a confidence level of 95%.

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Based on prior studies, about 10% of Californians are left-handed. Find the minimum sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of two percentage points, and use a confidence level of 95%.

The minimum sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of two percentage points and use a confidence level of 95%.

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z/2 = Z0.025 = 1.96

p = 10% = 10/100 = 0.1

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

ME =Z/2 * sqrt(p*(1-p)/n)

0.02 =  1.96 * sqrt(0.1*(1-0.1)/n)

0.02 /1.96 = sqrt(0.1*0.9 / n)

(0.02 /1.96)^2 =0.09 / n

n = 0.09 / (0.02 /1.96)^2

n = 864.36

n = 864

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