Question

Construct a confidence interval of the population proportion at the given level of confidence. x equals 160, n equals 200, 90 % confidence

The lower bound is ____. The upper bound is ____.

Answer 1

Here x = 160

n = 200

sample proporion = p^ = x/n = 160/200 = 0.8

Here we have to find 90% confidence interval

90% confidence interval = sample proportion +- margin of error

Margin of error = critical test statistic * standard error of proportion

standard error of proportion = sqrt (p^ * (1-p^)/n) = sqrt [0.8 * 0.2/200] = 0.0283

critical test statistic for 90 % confidence interval = NORMSINV(0.5 + 0.9/2) = 1.645

margin of error = 1.645 * 0.0283 = 0.0465

90% confidence interval = 0.8 +- 0.0465 = (0.753, 0.847)

Lower bound is 0.753

Upper bound is 0.847