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Estimating Risky Behavior 1. We would like to know what percent adult heterosexuals love m e is this mation. The AIDS Behavio
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Answer #1

(a)

\hat{p} = 170 / 2673 = 0.06360

n\hat{p} = 2673 * 0.06360 = 170

n(1- \hat{p} ) = 2673 * (1 - 0.06360) = 2502.997

Since, n\hat{p} and n(1- \hat{p} ) both are greater than 10, the assumption of normality are met.

(b)

Standard error of sample proportion, SE = \sqrt{\hat{p}(1-\hat{p})/n} = \sqrt{0.0636(1-0.0636)/2673} = 0.00472

Z value for 99% confidence interval is 2.576

Margin of error = Z * SE = 2.576 * 0.00472 = 0.0122

99% confidence interval is

(0.06360 - 0.0122, 0.06360 + 0.0122)

(0.0514, 0.0758)

(5%, 8%) (Rounded to nearest percentage)

We're 99% confident that the interval (5%, 8%) captured the true mean percentage of adult heterosexual with multiple partners.

(c)

99% of the intervals will contain p.

Number of confidence interval to contain p = 0.99 * 4215 = 4172.85 \approx 4173

Number of confidence interval to not contain p = 4215 - 4173 = 42

(d)

Using sample size of 700, number of heterosexuals in the club with multiple partners will lie in the range

(700 * 5%, 700 * 8%)

(35, 56)

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