Lab #3 – Normal Distribution & Confidence Intervals
Due Monday, April 24
Using the data on the following page, do the following computations using Stat Disk or your TI Calculator
as specified.
a)
b)
c)
d)
e)
f)
g)
h)
Find the mean, standard deviation, minimum, maximum, mode, median, first and third
quartiles for the data. In your report refer to these summary statistics and the charts
asked for in the next question and describe the data's characteristics. Discuss how the
data sets are similar and different and what type of calculations would be acceptable.
Calculate the IQR (3rd Quartile  1st Quartile) and discuss whether there are any outliers
in either data set based upon the criteria that are beyond 1.5IQR below Q1 or 1.5IQR
above Q3.
For each of the data sets using methods of normal probability find the values that
would be expected for the 1st, 2nd and 3rd quartiles using your TI (see page 246). In your paper
discuss these values and compare them to the values of the quartiles for these samples.
Use these values to support or refute your claims of normality.
Create a normal quantile plot (see section 5.7 of your text p. 285) and a histogram for each
data set (Twin 1 and Twin 2) using your TI Calculator (see bottom for instructions) and StatDisk
(use 10 classes for StatDisks histogram). Use this data to support the similarity and/or differences
and your assumptions about these data sets. (If you can’t connect TI & Print then you must draw by hand)
According to §5.7, for a data set to be considered approximately normal it must 1st have
only one mode, have no outliers, show symmetry and an “approximate” bell shape, and
then is a normal quantile plot shows an approximate straight line we can assume
normality. Using a)-c) give your assessment of the normality of these data sets. It must
be justified by you work.
Using both your TI and StatDisk find 85% confidence intervals for the population mean
of each data set assuming that the population standard deviation is unknown. In your
paper discuss the confidence intervals and how they are similar. Do mention the
assumptions that you are making in order to compute these confidence intervals Also in
your paper discuss the usefulness of confidence intervals and how they are superior to
sample means. (See p. 342-343 for info on StatDisk and TI. More info on TI below.)
Using both TI and StatDisk give a 90% confidence interval for the population mean of
each data set assuming that the population standard deviation is known to be 15. In your
paper, discuss how this changes the type of calculations that can be made for confidence
intervals. Mention the restrictions for finding confidence intervals.
Using StatDisk construct a 95% confidence interval for the standard deviation for the rug
data using Stat Disk (see p. 355 for information on using Stat Disk) . In your paper discuss the
assumptions necessary to make these calculations valid.
The questions above are meant to guide you in writing a paper about the data sets that you are analyzing. You should
be informing a reader about the information that you have learned in chapters 1 through 6. You should use the data in
the data sets and the summary and inferential statistics computed for each to make points about the things that you have
learned, particularly about normal or approximately normal and small versus large data sets.
TI Normal Percentiles: 1) 2nd Function Vars 2) InvNormal (percent below, mean, std.dev.)
Histogram w/ TI: 1) Enter the data into another register without repeats 2) In a separate register give the frequencies
of each data point 3) ZoomZoomStat (remember to get to Zstandard if you wish to graph in the rectangular coordinate system after this!) 4) 2nd Function for a
Stat Plot (possibly y= key) 5) Enter to get to Plot 1 6) Enter to turn Plot 1 on 7) Scroll down to Type and across to
the histogram (for Normal Quantile use the last in the 2nd row and the original data) 8) GRAPH 9) Screen Capture
with Connectivity
TI Confidence Intervals: 1) Stat 2) Test 3) Known  use ZInterval (Specify ), Unknown  use TInterval 4) Choose
Data 3) Give lists where data and frequencies are stored 4) Give CI level 5) Calculate