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# Statistics: Confidence Interval for the Scribe's use of caffeine

Confidence Interval or the lack of it...

It is the year 1581 A.D. At the Renaissance University (RU), I am the appointed CPA, Coffee Pot Attendant. It is a very important office sponsored by the Head Scribe.

I have taken this job very seriously, because I believe that I am the key to increased productivity of scribes at RU. Why, by mid-morning, many of my colleagues act as if they were ready for a nap. It is imperative that I restore productivity via a secret naturally-occurring molecule, caffeine...

In order to see if my secret molecule works, I have observed the time, in hours, a random selection of ten of my fellow scribes could stay awake copying over textbooks for students. Oh, yes, one fell asleep even before the official start of the workday!

1.9 0.8 1.1 0.1 -0.1
4.4 5.5 1.6 4.6 3.4

Now, I have to complete a report to the Head Scribe's Office on the effectiveness of my secret molecule so that UMUC can file for a patent at the United Provinces Patent and Trademark Office as soon as possible.

But I need the following information:

? What is a 95% confidence interval for the time my colleagues can stay awake on average for all of my colleagues?
? Was my secret molecule effective in increasing their attention span, I mean, staying awake? And, please explain.....

#### Solution Preview

First calculate the sample mean:

x-bar = (1.9+.8+1.1+.1+-.1+4.4+5.5+1.6+4.6+3.4)/10 = 2.33.

The sample standard deviation is calculated as follows:

s ...

#### Solution Summary

The confidence interval for the Scribe's use of caffeine is provided.

\$2.19