Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 40 had kids. Based on this, construct a 95% confidence interval for the proportion p of adult residents who are parents in this county.

Express your answer in tri-inequality form. Give your answers as decimals, to three places.

< p <  Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.

p =  ±±

Answer 1

point estimate of Sample proportion, = 40/100 = 0.4

Standard error of sample proportion, SE = = = 0.049

Z value for 95% confidence interval is 1.96

Margin of error = SE * Z = 0.049 * 1.96 = 0.096

95% confidence interval for the proportion p of adult residents who are parents in this county is,

0.4 - 0.096 < p < 0.4 + 0.096

0.304 < p < 0.496

p = 0.4 0.096