Question

A random sample of American toads were measured and the proportion of toads that were over 1 ounce in weight recorded. The measurements resulted in a sample proportion of p′=0.16, with a sampling standard deviation of σp′=0.02.

Write a 95% confidence interval for the true proportion of American toads that are over 1ounce in weight.

Answer 1

95% Confidence Interval for Proportions

= 0.16, 1 - = 0.84 , = 0.05, Standard error of proportion = 0.02

The Zcritical (2 tail) for = 0.05, is 1.96

The Confidence Interval is given by Z critical * Standard Error

Lower Limit = 0.16 - (1.96 * 0.02) = 0.1208    0.12

Upper Limit = 0.16 + (1.96 * 0.02) = 0.1992    0.20

Therefore the 95% CI for the true proportion is 0.12 < p < 0.20

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