In: Statistics and Probability
Out of 400 people sampled, 248 had kids. Based on this,
construct a 95% confidence interval for the true population
proportion of people with kids.
Give your answers as decimals, to three places
< p <
Solution :
Given that,
n = 400
x = 248
Point estimate = sample proportion = = x / n = 248/400=0.62
1 - = 0.38
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z/2 * ((( * (1 - )) / n)
= 1.96 (((0.62*0.38) / 400)
E = 0.048
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.62-0.048 < p < 0.62+0.048
0.572<p<0.668