Question

A reproductive clinic reported 43 live births to 207 women under the age of 40 who had previously been unable to conceive. Complete parts a through d below.

Find a 90​% confidence interval for the success rate at this clinic. (round to three decimal places)

Answer 1

Solution :

Given that,

n = 207

x = 43

Point estimate = sample proportion = = x / n = 43 / 207 = 0.208

1 - = 1 - 0.208 = 0.792

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 (((0.208 * 0.792) / 207)

= 0.046

A 90% confidence interval for population proportion p is ,

± E  

= 0.208  ± 0.046

= ( 0.162, 0.254 )