Math 311, Spring 2008, Lab 6
Due May 20th at 3:00 p.m.
The Tools
In this section you’ll learn the mechanics of 1-sample and 2-sample proportion tests
Inferences With Minitab:
Have Minitab compute two columns of 10,000 rows of data. Store this data in columns C1 and C2.
Choose the first (C1) from a B(1,.5) population and the second (C2) from a B(1,.2) population.
You’ll get a couple of columns of 0’s and 1’s.
Recall one does this by selecting Calc>Random Data> …. We will use these data in our tests
below.
Because the data in C1 came from a B(1,.5) population, about 50% of the data will be 1’s.
Similarly, because the data in C2 came from a B(1,.2) population, about 20% of the data will be 1’s.
1-sample proportion-test:
View the data in column C1 as a sample of size
10,000. We may use Minitab to compute both a confidence interval for the (true) population
proportion and perform a hypothesis test for the population proportion at one time!
a. Select Stat>Basic Statistics>1 Proportion…
b. Enter C1 for Samples in columns box
c. Click Perform hypothesis test.
d. Enter the value of the population proportion from the Null Hypothesis as the
Hypothesized proportion: (this is for the hypothesis test – the Alterative Hypothesis is
entered below). This time, use .45 (this is, in fact, pretty close to the true population
proportion of .5 – recall that the data came from a B(1,.5) distribution).
e. To set the confidence level select Options (this is for the confidence interval). 95% is
the default setting.
f. Notice that while you’re in the Options menu, you can also select equal to, greater than,
or less than for your Alternative Hypothesis. Since this is just practice, pick whichever
floats your boat.
g. Finally, select OK (twice) and get something like this:
Test and CI for One Proportion: C1
Test of p = 0.45 vs p not = 0.45
Event = 1
Variable
C1
X
49980
N
100000
Sample p
0.499800
h. Note: the hypotheses tested (p = 0.45 vs
output (I’ve highlight these for emphasis.)
i.
j.
95% CI
(0.496696, 0.502904)
p not = 0.45)
Exact
P-Value
0.000
are listed at the top of the
“X” gives the number of 1’s in the data – a 1 is considered a “success” and a 0 is a “failure.”
“Sample p” is our sample proportion ( p̂ ). Notice that it’s close to, but not exactly equal
to, .5. This is because of random error.
k. “Exact P-value” is the p-value from the hypothesis test. The p-value is low because our
null hypothesis was not correct – p is not .45. (I’ve highlight these for emphasis too.)
2-sample proportion tests:
We can perform 2-sample inferences by viewing the
data in columns C1 and C2 as samples from independent populations and by following the directions
below:
a. Select Stat>Basic Statistics>2 Proportions…
b. Select Samples in Different Columns (in this example, we’re going to compare the
samples in C1 and C2).
c. Enter C1 in First: and C2 in Second:
d. Select Options to set the confidence level and type of hypothesis test (1-sided vs. 2sided) and the value of the difference of the proportions in the null hypothesis.
e. Finally, select OK (twice) and get something like this:
Test and CI for Two Proportions: C1, C2
Event = 1
Variable
C1
C2
X
49980
19977
N
100000
100000
Sample p
0.499800
0.199770
Difference = p (C1) - p (C2)
Estimate for difference: 0.30003
95% CI for difference: (0.296062, 0.303998)
Test for difference = 0 (vs not = 0): Z = 148.20
P-Value = 0.000
Fisher's exact test: P-Value = 0.000
f. As above, “Sample p” gives the sample proportions for each sample.
g. Note Estimate for difference = difference of sample proportions = pˆ1  pˆ 2 .
h. Everything else should look familiar. Look at it. Do you know what each bit means? If
not, ask. If so, good.
i.
Important note: the samples from the two populations do not need to be in separate
columns. For example, suppose we were comparing the proportions of dead fish in
streams on the east coast vs. the west coast. If the dead fish data was in C1 and the
location (east or west coast) was in C2, then we could compare the dead fish proportions
by selecting the option Samples in one column and then entering C1 in the Samples: box
and C2 in the Subscripts: box.
You’ll need to try this in one of
following questions.
The Questions
In this section you’ll apply the techniques learned above
!!!BE CERTAIN TO READ EACH SITUATION CAREFULLY – THEY CONTAIN USEFUL CLUES!!!
Nutrition – platewaste. Again.
Just in case you hadn’t heard: A few years ago colleagues from the Family and Consumer Sciences
Department and I studied various factors that affect the amount of food elementary school children
eat during lunch.
Among other things, we were curious if the children’s Recommended Daily Allowances (RDA’s)
were being met at lunch. The results for each child at one of the schools are recorded in the file
RDAMet.mtw. Get this file now.
The non-obvious variable codes:
Ethnic Code: H = Hispanic, NH = Non-Hispanic
Entrée Type: mex = Mexican influenced (e.g. tacos), nonmex = not Mexican influenced (e.g. cheese
zombies).
T. Fat = total fat
S. Fat = saturated fat
Choles = cholesterol
Na+ = sodium
Fiber = fiber
Pro = protein
Fe+ = iron
Ca+ = calcium
Vit A = vitamin A
Vit C = vitamin C
A 1 was recorded if the student met or exceeded the RDA. A 0 was recorded otherwise.
1. Food service personnel would consider it “not horrible” if at least 50% of the kids consumed
at least 667 calories at lunch. Do we have evidence that this is true? Run the appropriate test
and then cut ‘n paste your results into a Word document. Clearly state your conclusion.
2. Is there a difference in the proportion of kids exceeding their daily allowance of saturated fat
when served Mexican influence entrees vs. non-Mexican influenced entrees? Cut ‘n paste
your results into a Word document. Clearly state your conclusion.
3. Is there a difference in the proportion of those exceeding the RDA of vitamin C between the
genders? Cut ‘n paste your results into a Word document. Clearly state your conclusion.
4. Pick something interesting from the data and run either a 1 or a 2-sample proportion test on
it. Yes, anything. You get to choose. I think this is an interesting data set and I hope you do
too. Report what you chose to investigate and then cut ‘n paste your results into a Word
document. Clearly state your conclusion.