Question

#7 Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 315 with 161 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.
95% C.I. =
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

Answer)

Given sample size n = 315

And point estimate p = 161/315

First we need to check the conditions of normality

That is if n*p and n*(1-p) both are greater than 5 or not

N*p = 161

N*(1-p) = 154

As both are greater than 5

Conditions are met and we can use standard normal z table to estimate the interval

From standard normal z table, critical value z for 95% confidence level is 1.96

So, z = 1.96

N = 315

P = 161/315

Margin of error (MOE) = Z*√{p*(1-p)/n}

MOE = 0.0552031091945

Confidence interval is given by

P-MOE < P < P+MOE

0.4559080019165 < P < 0.5663142203056