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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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ISBN:9780547587776
Author:HOLT MCDOUGAL
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Chapter11: Data Analysis And Probability
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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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