Question

In the National AIDS Behavioral Surveys sample of 2723 adult heterosexuals, 8 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? p~ = ……...

Give the plus four 93% confidence interval (±0.0001) for p:...… ⩽ p ⩽ ……….

Answer 1

Solution : Given that, n =  2723 x = 8 = x / n = 8 / 2723   = 0.0029 1 - = 1 - 0.0029 = 0.9971 At 93% confidence level the z is , = 1 - 903% = 1 - 0.93 = 0.07 / 2 = 0.07 / 2 = 0.035 Z/2 = Z0.035 = 1.812 Margin of error = E = Z / 2 * (( * (1 - )) / n) = 1.812 * (((0.0029 * 0.9971) / 2723 ) = 0.0019 A 93 % confidence interval for population proportion p is , - E < P < + E 0.0029 - 0.0019 < p < 0.0029 + 0.0019 0.0010 < p < 0.0048