Question

A survey of 2500 adult Americans found that 550 have donated blood in the past two years.

a) Obtain a point estimate for the population proportion of adult Americans who have donated blood in the past two years.

b) Verify that the requirements for constructing a confidence interval has been satisfied.

c) Construct a 90% confidence interval for the population proportion of adult Americans who have donated blood in the past two years.

Answer 1

Solution :

Given that,

n = 2500

x = 550

Point estimate = sample proportion = = x / n = 550/2500=0.22

1 -   = 1- 0.22 =0.78

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.22*0.78) /2500 )

E= 0.0136

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.22- 0.0136< p < 0.22+0.0136

0.2064< p < 0.2336

The 90% confidence interval for the population proportion p is : 0.2064, 0.2336