Question

A survey of 200 randomly chosen workers, 110 of them are female. Create a 99% confidence interval for the proportion of workers who are female based on survey. Please input the upper limit only. Use R to solve.

Answer 1

R-code

# Let p_hat be the proportion of female workers in the chosen sample
p_hat = 110/200
cat("\n Sample proportion of female workers = ",p_hat,"\n")

# sample size is nn
nn = 200

# For 99% confidence interval alpha = 0.01
alpha = 0.01

# Calculate the critical z-score
z = qnorm(1-alpha/2)

# Compute the CI
ci <- p_hat + c(-1,1)*z*sqrt(p_hat*(1-p_hat)/nn)
ci
cat("\n Lower Limit of Confidence interval ", ci[1],"\n")
cat("\n Upper Limit of Confidence interval ", ci[2],"\n")

R output

 Sample proportion of female workers =  0.55 

 Lower Limit of Confidence interval  0.4593872 

 Upper Limit of Confidence interval  0.6406128