Question

A company surveyed 2500 men where 1200 of the men identified themselves as the primary grocery shopper in their household.

​a) Estimate the percentage of all males who identify themselves as the primary grocery shopper. Use a 98​% confidence interval.

Answer 1

Formula for confidence interval estimate for single population proportions (percentage): p

for 98% confidence level = (100-98)/100 =0.02

/2 = 0.02/2 =0.01

Z/2 = Z0.01 = 2.3263

Number men surveyed : n = 2500

Number men who  identified themselves as the primary grocery shopper in their household : x= 1200

Sample Proportion of males who identify themselves as the primary grocery shopper : = 1200/2500 = 0.48

98​% confidence interval Estimate of the proportion of all males who identify themselves as the primary grocery shopper

98​% confidence interval Estimate of the proportion of all males who identify themselves as the primary grocery shopper = (0.456756,0.503244)

In percentage terms,

98​% confidence interval Estimate of the percentage of all males who identify themselves as the primary grocery shopper = (45.6756 % , 50.3244%)