#1 CI porportions

You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 435 randomly selected caterpillars observed, 57 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 435 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 413 randomly selected caterpillars observed, 47 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 (ANSWER) and (ANSWER) .

b. If many groups of 413 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About (ANSWER) percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about (ANSWER) percent will not contain the true population proportion.

PLEASE SEE ATTACHMENT.

You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 433 randomly selected caterpillars observed, 47 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and .

b. If many groups of 433 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 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 354 randomly selected caterpillars observed, 52 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and .

b. If many groups of 354 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 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 400 randomly selected caterpillars observed, 40 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and .

b. If many groups of 400 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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