Unformatted text preview: 11/30/2010 hw.2Pop.prop.4Topics.doc TwoPopulation Proportions 4 Topics Page 1 TWOPOP Proportions, 4 topics Revised 11/30/10 In order to get the Expected Values, you may USE the provided XLS file (on the website):
2SampProp.Compute.STUDENT.xls and choose which type of problem you are doing (2x2, 2x3,
3x4) by selecting the tab at the bottom of the Excel file. Be sure to fill in the values ONLY in the
body of the table (NOT the totals in the margins). You should create appropriate headings.
A. CASE 1: NOTE: The Z version of the difference in population proportions may already have been
assigned (hw.2Pop.Prop.ZOnly.pdf ). If so, no need to do it again, and thus skip part A and do
Parts B, C, and D. If it has NOT been assigned already, then of course do that part, too.
Company 1 (population 1) uses one way to make its employees aware of policies, and Company 2
(population 2) uses another way. We wonder if the two methods are different.
In a sample of 200 from company 1, 150 were aware of the policy change. In a sample of 100 from
company 2, 86 were aware of the policy change. Using Z, assume the standard deviation you will use
without modification is 0.049 and use this as the denominator without any adjustment.
CI: Estimate the difference between p1 and p2 by using a 95% confidence interval.
1.
This is a CI for what?
2.
Construct the CI.
3.
Give interpretation
HYPOTHESIS TESTING
Recall the 5steps are: Hypos; CV(s); DRule; Decision; Conclusion in terms of the problem.
1.
What is the symbol for the standard deviation?
2.
Use the regular method and 5 steps to test at α=0.05 whether the proportion at company 1 who were
aware is smaller than the proportion at company 2. (Of course, you have to state this as a difference:
p1  p2 [≥.or ≤ or > or <) 0 . (Note that in this class p1 will always be first, so we'll never have an
hypothesis of the form p2  p1 .) Provide a fully completed graph. Pay particular attention to the
conclusion in terms of the problem. NOTE THAT FOR TWO POPULATIONS WE WILL
TYPICALLY HAVE A TWOTAILED TEST OF THE DIFFERENCE = 0 VERSUS IT DOESN'T
= 0. HOWEVER, AS A REMINDER OF PREVIOUS HYPOTHESES, THIS TIME WE'LL DO A
ONETAILED TEST. THIS IS ONE OF THE HYPOTHESES: p1  p2 < 0 AND YOU DECIDE
3.
4.
B. WHICH HYPOTHESIS IT IS.
Compute the pvalue and show where it is on the graph.
Do the test using STS and label the graph. (Using Z we can do both regular and STS but here we only
are doing STS. With χ STS is the only choice – there is no regular method).
Same data as part A, but now using χ2: assume df=1 . Test whether the two population proportions
are the same (which is different from the previous problem), and it is a 1tailed test. (You'll need to
rewrite the given information as a contingency table, as we had in class, where do not use proportions
directly, but rather use the actual raw data. How to do this: for sample 1 the sample size is 200 and
150 were aware, so 50 were not aware. Sample 2 of 100, 86 were aware and 14 were not aware.)
a.
For the χ2: Have we met the assumption about expected values? EACH expected value must be
≥ 5 for this method to be valid.
b. Note that there is no "regular" method; the only hypothesis testing method for this case is STS. c. Compute the pvalue and show it on the graph. Continued on next page 11/30/2010 TwoPopulation Proportions 4 Topics Page 2 C. New Data and new problem: Here population 1 is Honda owners, population 2 is Toyota owners, and
population 3 is Dodge owners. A sample was drawn from each population and each was asked
whether he or she was satisfied with their car. Of 200 Honda owners, 180 were satisfied; of 300
Toyota owners, 260 were satisified; of 100 Dodge owners, 79 were satisfied. Test at α=0.10 whether
the 3 population proportions who are satisfied are the same. Use the 5step method. df = (2 rows1)(3
cols1) = 2. Fill out the graph fully, and compute the pvalue. This is a onetailed test. Compute the pvalue and show it on the graph. D. Test at α = 0.05 whether the two factors are independent. There are 4 car manufacturers, and each
produces 3 sizes of car: small, medium, and large. If the factors are dependent, then buyers would
tend to pick one of the manufacturers if they wanted small cars, and would tend to pick a different
manufacturer if they wanted a larger car, and so on. If the factors (car make versus car size) are
dependent, then we would reject Ho. Do the 5step process (only STS exists) and fill out a graph.
Compute the pvalue and show it on the graph.
A sample of 1000 purchasers gave the following information, which is the number of people who
bought a certain size car from a certain manufacturer. Are the factors (car make versus size)
independent? Small
Medium
Large
Totals Honda
157
126
58
341 Toyota
65
82
45
192 Ford
181
142
60
383 Dodge
38
31
15
84 Totals
441
381
178
1000 df = (3 rows1)(4 cols1) = 6, and it is a onetail test. [Note that we could have any number of rows
and any number of columns when testing for independence.] ...
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 Winter '11
 kim
 Statistics, Variance, Null hypothesis

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