A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%? A previous study indicates that the proportion of households with two cars is 25%.A) 4 B) 1132 C) 1842 D) 1382

Answer: Sample size n = 1382 so correct option is D) 1382Step-by-step explanation:given data confidence level = 99 %margin of error = 3% probability = 25 %to find outHow large a sample size neededsolutionwe know here P = 25 % so 1 - P = 1 - 0.25 1 - P  = 0.75 and we know E margin of error is 0.03 so value of Z for 99% α = 1 - 99%   = 1 - 0.99 α  = 0.01 and  [tex]\frac{\alpha}{2}[/tex] = [tex]\frac{0.01}{2}[/tex] [tex]\frac{\alpha}{2}[/tex]  = 0.005 so Z is here [tex]Z_(\frac{\alpha}{2})[/tex] = 2.576 so sample size will be Sample size n =  [tex](\frac{(Z_(\frac{\alpha}{2})}{E})^2 * P * (1-P)[/tex]put here value Sample size n = (\frac{2.576}{0.03})^2 * 0.25 * 0.75 Sample size n = 1382 so correct option is D) 1382