Question

You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 356 randomly selected caterpillars observed, 42 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 356 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.

Answer 1

Answer:-

Given That:-

You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 356 randomly selected caterpillars observed, 42 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 .?

Level of significance,

Number of items of Interest , X = 42

Sample Size, n = 356

Sample Proportion,

Z-value = [excel formula = NORMSINV]

Standar Error,

margin of error,

99% confidence interval is

Interval Lower Limit=

Interval Upper Limit=

99% confidence interval is

b. If many groups of 356 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.

About 99% percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about 1 percent will not contain the true population proportion