Question

In a sample of 2000 American adults, 500 said they believed in astrology.

1. What is the point estimate of the corresponding population proportion?
2. Make a 90% confidence interval for the population proportion.

Answer 1

Solution :

Given that

Point estimate = sample proportion = = x / n = 500/2000=0.25

1 -   = 0.75

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z  0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.25*0.75) / 2000)

E = 0.016

A 90% confidence interval proportion p is ,

- E < p < + E

0.25 - 0.016< p < 0.25+0.016

0.234< p < 0.266