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Statistics and Confidence Intervals Deviations

Work on an Excel spreadsheet with results linked to data using Excel functions and cell addresses. To derive the confidence intervals for the mean with known standard deviation, use the z table from Table E.2 or =normsinv.
1) The Harvard class of 2009 had a reunion attended by 36 members. It was determined that they had married an average of 2.6 times. Assume that the standard deviation is 0.3. Help the dean construct a 99% confidence interval for the mean Harvard alumni marriage rate.
2) Assume that the standard deviation of college student IQs is 10. A random sample of 100 students from a college showed a mean IQ of 112. Compute a 95% confidence interval for the mean IQ of students attending that college. The confidence interval for the mean with unknown standard deviation (Use t from Table E.3 or =tinv)
3) The nicotine content of five cigarettes of a brand were 21, 19, 23, 19, and 23 milligrams. Compute a 0.99 confidence interval for the mean. Compute a 0.99 confidence interval for the total nicotine content in 1000 cigarettes.
7) Out of a group of 15,000 degree candidates of the University of North Carolina at Chapel Hill, a random sample of 400 showed that 20% of the students have an earning potential exceeding $65,000 annually. Compute a 95% confidence interval for the proportion of students with earning potential exceeding $65,000 annually.

Solution Preview

The confidence interval for the mean with known standard deviation (Use z from Table E.2 or =normsinv) is in the following.
1) The Harvard class of 2009 had a reunion attended by 36 members. It was determined that they had married an average of 2.6 times. Assume that the standard deviation is 0.3. Help the dean construct a 99% confidence interval for the mean Harvard alumni marriage rate.
Answer
The confidence interval is given by , where = 2.6, ? = 0.3, n = 36, = 2.575829304
That is,
= (2.4712, 2.7288)
Thus with 99% confidence we can claim that population mean Harvard alumni marriage rate is within (2.47, 2.73) times.
Details
Confidence Interval Estimate for the Mean

Data
Population Standard Deviation 0.3
Sample Mean 2.6
Sample Size 36
Confidence Level 99%

Intermediate Calculations
Standard Error of the Mean 0.05
Z Value -2.575829304
Interval Half Width 0.128791465

Confidence Interval
Interval Lower Limit 2.47121
Interval Upper Limit 2.72879

2) Assume that the standard deviation of college student IQs is 10. A random sample of 100 students from a college showed a mean IQ of 112. Compute a 95% confidence interval for the ...

$2.19