# Proportion and and Confidence Intervals

a. In your sample, what is the proportion of males who have brown ("Brown" only) eyes?

3 of 8 males have brown eyes. (.375)

b. What is a 95% confidence interval on the proportion of males with brown eyes in the "population" (The population here is of all men.)

c. In your sample, what is the proportion of females who have brown ("Brown" only) eyes?

5 of 22 females have brown eyes. (.227)

d. What is a 95% confidence interval on the proportion of females with brown eyes in the "population" (The population here is of all women.)

e. Perform a hypothesis test on H0: In the population, the proportion of females with brown eyes equals 50%. What is the P-value for a 2-sided test of this null hypothesis?

f. Perform a hypothesis test on H0: In the population, the proportion of men with brown eyes equals the proportion of women with brown eyes. What is the P-value for a 2-sided of this "null hypothesis" (The proportions here are of all men and of all women, resp.)

g. What is the difference in proportions in your sample of men who have brown eyes and women who have brown eyes? (The proportions here are of all men and of all women, resp.)

h. What is a 95% confidence interval for the difference in proportions of men who have brown eyes and women who have brown eyes in the population? (The proportions here are of all men and of all women, resp.)

#### Solution Preview

a. The proportion of males who have brown ("Brown" only) eyes is 3/30 = 0.1

b. 95% confidence interval on the proportion of males with brown eyes in the population is given as

Sample Proportion (P) ±Z(Critical value)*sqrt(P*(1-P)/n)

Here we have

Sample Proportion (P) = 0.1

Z(Critical value at 0.05 level of significance) = 1.96

Sqrt(0.1*(1-0.1)/30) = 0.054772

Lower Limit = 0.10 - 1.96* 0.054772256 = 0.00

Upper Limit = 0.10 + 1.96* 0.054772256 = 0.2074

A 95% confidence interval for the population is (0.00, 0.2074)

c. The proportion of females who have brown ("Brown" only) ...

#### Solution Summary

This solution is comprised of a detailed explanation for confidence interval for proportion using Excel. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of 95% confidence interval for proportion with the help of excel. Formulas are added in word file for better understanding and interpretation is given at the end of every question.