You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 371 randomly selected caterpillars observed, 45 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 371 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.
You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 371 randomly selected caterpillars observed, 45 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 371 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.
Solution:
Given information:
n= 371 Sample of caterpillars
x = 45 caterpillar lived to become butterflies.
Sample proportion of caterpillar lived to become butterflies.
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