Question

1. In certain areas AIDS-HIV epidemic may a concern. A sample of 176 people were examined for AIDS-HIV and 44 were found to be infected by AIDS-HIV. We will compute a 99 percent confidence interval for the proportion p of people who were infected by AIDS-HIV. Compute the margin of error e in estimating p at 99 percent level of confidence. Give the Margin of Error e, Left end point, Right end point, and the Conservative Margin of Error E:

   MOE = e =? LEP =? REP = ? C − MOE = E =?

Answer 1

= 44/176 = 0.25

At 99% confidence interval the critical value is z^* = 2.58

Margin of error E = z^* * sqrt((1 - )/n)

                                = 2.58 * sqrt(0.25 * (1 - 0.25)/176)

                                = 0.0842

The 99% confidence interval for population proportion is

+/- E

= 0.25 +/- 0.0842

= 0.1658, 0.3342

LEP = 0.1658

REP = 0.3342