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You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 435 randomly selected caterpillars observed, 47 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% 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 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 435 randomly selected caterpillars observed, 47 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% 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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 435 randomly selected caterpillars observed, 47 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% 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.
Transcribed Image Text:You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 435 randomly selected caterpillars observed, 47 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% 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.
Expert Solution
Step 1

Solution:

a.

Let X be the number of caterpillars that eventually become butterflies and n be the sample number of caterpillars.

From the given information, X=47 and n=435.

Step 2

The sample proportion is

Statistics homework question answer, step 2, image 1

The confidence level is 0.90.

Statistics homework question answer, step 2, image 2

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