# Confidence Interval and Sample Size Calculations

1. Of 300 people waiting lunch at a department store cafeteria, 102 had dessert. What is the confidence associated with a Rao score interval of length .1 (i.e., margin of error .05)?

2. Calculate the sample size necessary to estimate the proportion of drivers that exceed the spend limit on a stretch of a road between Bakersfield and Los Angeles within a margin of error of .04 with a 99% confidence.

3. How large a sample is necessary to estimate a politician's approval rating with a margin of error of 3.5% if we want 90%, 95%, and 99% confidence?

See the attached file.

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#### Solution Preview

Please refer to the attachment.

1. Of 300 people waiting lunch at a department store cafeteria, 102 had dessert. What is the confidence associated with a Rao score interval of length .1 (i.e., margin of error .05)?

Solution:

The margin of error, for confidence interval for proportion, is given as follows:

E=zα2 p1−pn

Given:

Proportion of Success, p=102300=0.34

Sample Size, n=300

Margin of ...

#### Solution Summary

The solution calculates the confidence interval and sample size of the given problem.