Question

In a survey of

2320

​adults,

725

say they believe in UFOs. Construct a

99 %

confidence interval for the population proportion of adults who believe in UFOs.

A

9999​%

confidence interval for the population proportion is

​(nothing ​,nothing ​).

​(Round to three decimal places as​ needed.)

Answer 1

Solution:

Given that x = 725, n = 2320
The sample proportion is the number of successive divided by the sample size:

p̂ = x/n = 725/2320 = 0.3125

α = 0.01
Z_α/2 = Z_0.005 = 2.576
  
The boundaries of the confidence interval are then:
p̂ ± Z_α/2 .√p̂(1-p̂)/n = 0.3125 ± 2.576 .√0.3125(1-0.3125)/2320
= 0.3125 ± 0.0248
= [0.2877, 0.3373]