In: Statistics and Probability
If n = 400 and ˆpp^ (p-hat) = 0.25, construct a 95% confidence
interval.
Give your answers to three decimals
Solution :
Given that,
n = 400
Point estimate = sample proportion = = x / n = 0.25
At 95% confidence level the z is ,
Z/2 = Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z/2 * ((( * (1 - )) / n)
E = 0.042
A 95% confidence interval for population proportion p is ,
0.25 -0.042< p < 0.25+0.042
0.208< p < 0.292