Question

In a survey of 1000 US adults, 490 opposes allowing transgender students to use the bathroom of the opposite biological sex. Construct a 90% confidence interval for the population proportion of adults who oppose allowing transgender students to use the bathroom of the opposite biological sex.

Answer 1

Solution :

Given that,

n = 1000

x = 490

Point estimate = sample proportion = = x / n = 490 / 1000 = 0.49

1 - = 1 - 0.49 = 0.51

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.49 * 0.51) / 1000)

= 0.026

A 90% confidence interval for population proportion p is ,

± E   

= 0.49  ± 0.026

= ( 0.464, 0.516 )