Question

You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 384 randomly selected caterpillars observed, 52 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 384 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About 95 percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about 5 percent will not contain the true population proportion.

Answer 1

From the given information,

To answer part-a,

n= 384

p= 52/384= 0.1354

Hence,

By using confidence interval calculator,

The required 95% confidence interval is given by,

0.1012 < P < 0.1696

Part-b is correct.

Thank you.

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