Question

A 2016 study done in Germany was doing research on parents and wanted to determine the percent of parents that regret having children. To do so, they randomly selected 400 parents and found that 36 of them regret having children. Construct and interpret a 99% confidence interval for the proportion of parents that regret having children. Round your answers to two decimal places.

Answer 1

Solution :

Given that,

n = 400

x = 36

Point estimate = sample proportion = = x / n =36/400=0.09

1 -   = 1- 0.09 =0.91

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

  Margin of error = E = Z/2   * (((( * (1 - )) / n)

= 2.576* (((0.09*0.91) / 400)

E = 0.04

A 99% confidence interval proportion p is ,

- E < p < + E

0.09-0.04 < p < 0.09+0.04

0.05< p < 0.13

(0.05 , 0.13)