In: Statistics and Probability
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%.
SOLUTION:
From given data,
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
Please thumbs-up / vote up this answer if it was helpful. In case of any problem, please comment below. I will surely help. Down-votes are permanent and not notified to us, so we can't help in that case. |