Kyle Daniele
Extra Credit
Example 1
Look at the 95% confidence interval of a proportion, p, if phat=.3 and
a. n = 30
95% CI = (.13602, .46398)
b. n = 100
95% CI = (.21018, .38982)
Since the width of the interval in this case is 2[z(1c)/2(square root of phat times qhat
divided by n)], the increase from n = 30 to n = 100 results in a narrower confidence
interval since all other quantities remain the same.
Example 2
If a sample proportion is given as .35 with a margin of error of +3%, find the 95%
confidence interval for the population proportion.
Solution: .35 + .03
95% confidence interval is (.32, .38)
Example 3
A simple random sample of 100 eighth graders at a large suburban middle school
indicated that 83% of them are involved with some type of afterschool activity. Find the
margin of error for this sample result if we are to have 90% confidence in the results.
Solution: Check Assumptions.
Simple random sample?
Given
Large population?
Given
n*phat>10 and n*qhat>10
100(.83) = 83; 100(.17) = 17
Therefore, the margin of error for this sample with 90% confidence is
Z(1C)/2(square root of phat times qhat divided by n)
1.645(square root of .83(1.83) divided by 100) = .062
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 Spring '09
 CHANG
 English, Statistics, Normal Distribution, Standard Deviation, Simple random sample

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