You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 436 randomly selected caterpillars observed, 47 lived to become butterflies. a.  With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and . b.  If many groups of 436 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 436 randomly selected caterpillars observed, 47 lived to become butterflies.

a.  With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and .

b.  If many groups of 436 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

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