Question

22.50 S-AQ) In the National AIDS Behavioral Surveys sample of 2563 adult heterosexuals, 7 respondents had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. You should not use the large-sample confidence interval for the proportion p in the population who share these two risk factors. The plus four method adds four observations, two successes and two failures.

What is the plus four estimate pˆp^ (±0.0001) of p? pˆp^ = ____

Give the plus four 96% confidence interval (±0.0001) for p:    ⩽p⩽⩽p⩽  .__

Answer 1

Solution :

n = 2563

x = 7

= x / n =7 / 2563 = 0.0027

1 - = 1 - 0.0027= 0.9973

At 96% confidence level the z is ,

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z/2 = Z0.02 = 2.050

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

= 2.050 * (((0.0027 * 0.9973) / 2563)

= 0.0021

A 96 % confidence interval for population proportion p is ,

- E < P < + E

0.0027 - 0.0021 < p < 0.0027 + 0.0021

0.0006 < p < 0.0048