Answer to Question #164924 in Statistics and Probability for Sowmya

Question

In a study of perception, 80 men are tested and 7 are found to have red/green color blindness. What sample size would be needed to estimate the proportion of male red/green color blindness if we wanted 96% confidence that the sample proportion is in error by no more than 0.03?

Answer 1

$\alpha= 100-96=4\%=0,04$

$\frac{\alpha}{2}=0.02$

$\text{of z-table } z_{0.02}=2.055\text{ value for }1-\alpha =0.98$

$\hat{p}=\frac{7}{80}=0.875;\hat{q}=1-\hat{p}=0.125$

$n=\frac{z^2_{0.02}\hat{p}\hat{q}}{E^2}=\frac{2.055^2*0.875*0.125}{0.03^2}\approx513$

Answer:513