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In Class Quiz: An Excel – Based Interpretation of Confidence
The purpose of this quiz is to get at the true meaning of “confidence” concretely (statistical
confidence, that is; I figure everyone has their own image of what “nonmathematical confidence” looks like in
the world around them). We’re used to that word “confidence”. Goodness knows we see it enough – here
are two instances I noticed “95% confidence” in just this week!
But what, exactly does “95% confident” mean? That’s what this quiz aims to do: shed light on the idea
of confidence in a very concrete way. We’ll use Excel to help!
In this quiz, we’ll approximate the average birth weight of an American baby (ABWAB), using the ideas
of confidence intervals (CIs). Please start by opening the spreadsheet “weights.xlxs” (the link next to the link
from which you opened this page). You’re viewing the ABWABs of 20 randomly selected American newborns1,
along with a histogram of that sample. Let’s start by getting that mean and standard deviation filled in! Type
=AVERAGE(B4:U4) in cell D8 and =STDEV(B4:U4) in cell D9. Don’t forget the equals signs!
Now – press
key a few times. Each time, you get a new “sample of 20 babies”. You see how their
weights change each time? The histogram, x̄ and s all change, as well.
From these data, I’d like you to construct some 95% CIs for the ABWAB, using Excel. We’ll use the
“confidence” command to get the Margin of Error (MOE) of our sample of size 20. In cell D11, type this in:
 The first value, 0.05 is called the significance. It’s the decimal complement of the confidence.
Since the significance is set at 5% the confidence must be 95%.
 The second value is a cell reference to the sample standard deviation, which you placed in cell
D9.
 The third number is the sample size.
Excel only needs these three values for a MOE calculation; we’ll see more later in class!
Now that you have a mean and a MOE, you can construct the CI’s! Tech note: the two endpoints of
any confidence interval are often called the “LCL” (“lower confidence limit”) and “UCL” (“upper confidence
limit”). Let’s form those now!
Actually, what you’re looking at is a sample of 20 numbers I generated using the “known” values of  and  for the weights of
newborns. By “known”, I mean that, after hundreds of millions of births, doctors have pretty much figured that they have the
parameter values of  and . I used Excel’s random number generator (and something called the Box – Muller normal
approximation) to allow for natural fluctuations from baby to baby; every time you press ENTER, the randomizer will kick in, and
you’ll get 20 new baby weights. If you’re interested, click in any of the weight cells to see the function.
1
Type =D8-D11 in cell C15, and =D8+D11 in cell D15. Cells C15 and D15 are now your 95% CI
endpoints! Cool, huh?
Go ahead and press
a few more times and see how everything changes. When you’re bored of
doing that, I want you to gather some 95% CI’s!
1. (8 points) Give me twenty 95% CI’s for the ABWAB. Press
at least once after constructing each CI
so that you get new baby data each time. Round values to the nearest hundredth’s place. You can
most likely just copy and paste them into a Word document.
OK...so you have 20 CI’s. Great! Now, we need to drive home what the term “95% confident” really
means...
…it is “known” that the ABWAB is 7 pounds, 11 ounces (or 7.67 pounds). Take a look at your CI’s:
2. (2 points) What percent of the CI’s that you constructed contain the value  = 7.67?
(wait’ll you see what happens when we collate our data.  )
It gets better...please click on the tab “Randomized
Results” (it’s down near the bottom of the workbook). Here, I’ve created 20 CI’s (identical, in construction, to
the 20 you just created). However, instead of giving you the values of the endpoints, I’ve done the CI’s
graphically.
You’ll also see a vertical line through 7.67; this line represents the value of . Do you see how many of
These CI’s contain ? I did this little exercise, too, and got the results at
f
Percent that contain 
right. Check this out:
80
1
 The mode of these values? 95%.
90
3
 The median of these values? 95%.
95
10
 The mean of these values? A little above 95%.
100
8
Wowsers! This means that, if we repeatedly construct CI’s around randomly selected data sets, we
can expect around 95% of them to contain the true population mean.
And that, my fine friends, is the definition of confidence!
Make sure you submit your 20 CI’s (from question number 1) and your percent (from question number
2)!