Question

Out of 320 people sampled, 240 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

• 0.85 < pp < 0.65
• 0.8 < pp < 0.7
• 0.7 < pp < 0.8
• 0.93 < pp < 0.57
• 0.9 < pp < 0.6

Answer 1

Solution :

Given that,

n = 320

x = 240

Point estimate = sample proportion = = x / n = 240/320=0..75

1 -   = 1- 0.75 =0.25

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 (((0.75*0.25 )/ 320)

E = 0.047

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.75-0.047 < p <0.75+0.047

0.7< p < 0.8

The 95% confidence interval for the population proportion p is : 0.7< p < 0.8