Confidence Intervals

Please answer all questions using Microsoft Word, Excel, and the StatCrunch/Graphing

Calculator. Use Word to write-up your solutions while copy/pasting graphs from Excel

and StatCrunch/Graphing Calculator. You may use this sheet as a guide. Please submit

projects the day of the exam: Good luck!

1) A. Generate 50 random samples of n=30 from a normal population with =69 and

=3.Construct 90% confidence intervals for each of the 50 samples. These

confidence intervals will appear in the output session window. Copy/paste them

into your excel spread sheet and print the spreadsheets to turn in.

B. Look at the confidence intervals. How many of your intervals failed to correctly

estimate ?________(Hilite these intervals on your print out)

How many of your intervals actually did contain ?_________

C. What percentage of your intervals contained ?__________

D. Based on the confidence level used in this example, what percentage of the

intervals did you expect to contain ?

E. How does your actual percentage compare with the percentage you expected

based on the confidence level? How has this experiment helped you understand

what level of confidence means? Explain.

F. Calculate five 95% confidence intervals and calculate the width of the intervals

by subtracting the lower limit from the upper limit and rounding your answer to

the nearest hundredth. What did you discover?

G. For the first five 90% confidence intervals that you created calculate the width

of the intervals and round to the nearest tenth. What did you discover?

H. How does the width of the 95% confidence interval compare to the width of

the 90% confidence intervals? Show/demonstrate/copy /paste what you've seen.

2. For this example, you will enter the data directly into your spreadsheet. Here is

a random sample of resting heart rates for 20 male athletes between the ages of

18 to 25:

58,67,63,65,59,57,51,64,59,54,65,56,59,58,62,64,55,59,61,55

You are interested in knowing a confidence interval for , the average resting

heart rate of all male athletes of this age group.

a) What assumptions are needed in order to use T procedures(make sure you

find all assumptions listed in the text)? Are they met?

Include a histogram and boxplot of the data.

b) Construct a 99% confidence interval for . Interpret.

Make a statement about .

3. Suppose you are interested in estimating the average salary for

biostatisticians in Connecticut. You obtain a random sample of

25biostatisticians hired during the last 5 years. The sample data appeared to

be approximately normally distributed with no outliers. The average salary for

the sample is $45000 and the sample standard deviation is $3150.

A) Construct a 95%confidence interval for the true average salary for newly

hired biostatisticians in Connecticut.

B) How large of a sample is needed to estimate within $2000?

4) Some say Hillary Clinton is unstoppable for 2016. A recent poll indicates that

586/1000 voters will favor her in the next election.

A) Create a 90% confidence interval for P ( the population proportion) and interpret.

B) Based off of that interval is there strong evidence to say she will win?

C) How large of a sample is needed for a desired margin of error of 2% using 90%

confidence and 586/1000 as a point estimate for P.