Question

Of 1428 people who came into a blood bank to give blood, 303 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. What is the 95% confidence interval for this probability estimate?

Answer 1

Solution :

Given that,

n = 1428

x = 303

Point estimate = sample proportion = = x / n = 303/1428=0.212

1 -   = 0.788

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.212*0.788) /1428 )

E = 0.021

A 95% confidence interval f is ,

- E < p < + E

0.212-0.021 < p < 0.212+0.021

(0.191 , 0.233)