MHB Confidence interval to stay awake while listening to the Dean

[sfm1985]

Confidence Interval or the lack of it...

It is 1581 Anno Domini. At the Undergraduate School of UMUC, besides Assistant Academic Director of Mathematics and Statistics, I am also the Undergraduate School-appointed CPA, Coffee Pot Attendant.

It is a very important office sponsored by the Holy See.

I have taken this job very seriously, because I believe that I am the key to increased productivity at the Undergraduate School. Why, by mid-morning, many of my colleagues act as if they were

It is imperative that I restore productivity via a secret naturally-occurring molecule, caffeine...

In order to see if my secret molecule works, a random sample of ten colleagues who had the coffee before the Dean's meeting was selected.

I have observed the time, in hours, for those 10 colleagues to stay awake at the extremely long-winded Dean's meeting as soon as it started. Oh, yes, one fell asleep even before the meeting started!

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 Provost'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. Oh, yes, I am waiting for a handsome reward from the Provost... 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? (Show the work to get full credit)
•Was my secret molecule effective in increasing their attention span, I mean, staying awake? And, please explain...This is what I have so far, after this I am stuck:
1.9 4.4
0.8 5.5
1.1 1.6
0.1 4.6
-0.1 3.4


Mean 2.33
SD 2.002249

In order to find the mean I took:
1.9+.8+1.1+.1+-.1+4.4+5.5+1.6+4.6+3.4= 23.3/10= 2.33

[/B]

 

[Euge]

Welcome, sfm1985!

If the sample mean, $\bar{x}$, and sample variance, $s$, are known, then a 95% confidence interval takes the form

$$\left(\bar{x} - 1.96\frac{s}{\sqrt{n}}, \bar{x} + 1.96\frac{s}{\sqrt{n}}\right)$$

where $n$ is the sample size. In your case, $n = 10$. Plug in your values of $\bar{x}$ and $s$ into this formula to compute the confidence interval.