252hwk 01/06/01
1999 last computer problem
(The problem was 11.26 in the last edition of the text. The instructions below can give you an idea
of what was expected.)
Hours of
Maintenance
1.0
3.1
17.0
14.0
6.0
1.8
11.5
9.3
6.0
12.2
Number of
Copy Machines
1
3
10
8
5
1
10
5
4
10
Months of
Experience
12
8
5
2
10
1
10
2
6
18
I will not give you specific instructions to try to run this. You
need to name columns for the data given in the test as well as a resid
and pred column. You should begin with the command
Brief 3
This will give you a predicted value for each observation (under ‘fit’) and a standard deviation needed for a
confidence interval for y when you do a regression.
Let’s say you call your variables ‘X1’, ‘X2’, ‘X3’ and ‘Y’ (I didn’t). To multiply ‘X1’ and ‘X2’ together
and put the result in ‘X3’, use
Let ‘X3’ = ‘X1’*’X2’
To do a plot of ‘Y’ against ‘X1’ use
Plot ‘Y’*’X1’
To do a regression of ‘Y’ against all 3 independent variables use
Regress ‘Y’ on 3 ‘X1’‘X2’‘X3’ ’resid’ ’pred’
(These are all single quotes.) The number 3 here
indicates the number of independent variables and should be changed when you change the number of
independent variables. If you do not make the change, some of your data could be destroyed.
To do a stepwise regression of ‘Y’ against all 3 independent variables use
Stepwise ‘Y’‘X1’‘X2’‘X3’
Do the following regressions:
Hours of Maintenance against Number of Copy Machines
Hours of Maintenance against Months of Experience
Hours of Maintenance against Number of Copy Machines and Months of Experience
Hours of Maintenance against Number of Copy Machines, Months of Experience and Interaction
After each regression plot Hours of Maintenance against ‘pred’ to see how well you did. If you have a
perfect prediction, your graph will be a 45-degree line.
When you are through try a stepwise regression against the three independent variables. The results
surprised me. You should be able to verify that the first regression gives the same coefficients as one that
you already have run. But what about the next one? I should confess that I have gotten completely different
results from those in the answer book.
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252hwk 01/06/01
1999 Graded Assignment 1
Problem 1: Using the computational formula, find the sample variance of the following data and use it to
compute a 95% confidence interval for the mean.
x
5
-7
11
13
15
12
11
3
Problem 2: Find a symmetrical interval about the mean for the distribution x ~ N 5,6 with a probability of
84%.
Problem 3: Using the value of z that you used in Problem 2, find an 84% confidence interval for the mean
if x  7.035 , n  16 and   1.7 .
1999 Graded Assignment 2
Problem 1: Which of the following could be a null hypothesis?
  3,   3,   3,   3,   3 ,   3 , x  3, x  3 , x  3, x  3, x  3 , x  3
Problem 2: A man walks into a bar. He drinks 15 bottles of beer. These bottles are supposed to contain 12
ounces of beer with a population standard deviation of 0.2 ounces. On the basis of the man's condition when
he leaves the bar, we conclude that the sample mean for the bottles was 11.80 ounces. Test the hypothesis
that the population mean for these bottles was 12 ounces. Assume that the confidence level is 95%.
a) state your null and alternative hypotheses.
b) Find critical values for the sample mean and test the hypothesis.
c) Find a confidence interval for the sample mean and test the hypothesis.
d) Use a test ratio for a test of the sample mean, find its p-value and use the pvalue to test the hypothesis.
Problem 3: (Dummeldinger) According to the Chronicle of Higher Education Almanac, the average tuition
(plus fees) for a private college in 1992 was $9083. A survey of 40 schools gave a sample mean of $9750
and a sample standard deviation of $1750.
a) Test the validity of the Almanac's statement using a confidence level of 95%.
b) Find an approximate p-value for the statement.
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252hwk 01/06/01
1999 Graded Assignment 3
Problem 1: Do Problem 15.59 in Excel as follows.
Use columns A, B, C, and E on the Excel spreadsheet for data
In the first row of A, B, C and D put in T1, T2, T3, T4
Now put in the data in columns A, B, C and E, skipping column D
To fill column D in cell D2 write =E2 after your 'enter' this cell should read '12'
Use the 'edit' pull-down menu and 'copy' cell D2
Use the 'edit' pull-down menu and 'paste' in cells D3 through D6. Now column D will be identical to E
except for the heading. Save your data as data59.xls
Use the 'tools' pull-down menu and pick 'data analysis'
Pick 'ANOVA: Single Factor. Set input range to $A$1:$D$6 select 'New worksheet ply' and 'columns' ,
check 'labels in first row' hit 'OK' and save your results as result59.xls
Take the last digit of your social security number (if it's zero, use 1). Go back to your original data or use
the 'file' pull-down menu to open data59.xls.
To fill column D this time in cell D2 write =E2-x replacing x with the last digit of your social security
number.
Use the 'edit' pull down menu and 'copy' cell D2
Use the 'edit' pull down menu and 'paste' in cells D3 through D6. Now column D will be less than E by the
amount of your value of x. Save your data as data59a.xls.
Run the ANOVA again and save your results as result59a.xls
Submit the data and results with your Social Security number. Indicate what hypotheses were tested and,
what the p-value was and whether, using the p-value, you would reject the null if (i) the significance level
was 5% and (ii) the significance level was 10%, explaining why. You will have two answers for each of
your two problems.
For your second ANOVA do a normal and a Scheffe confidence interval for 1   4 , using the data in your
ANOVA output.
Problem 2: Do the following problems. In a-d you are only asked to state hypotheses.
a) If 1 was the average amount spent by pharmaceutical firms in 1998 and  2 was the average amount
spent by pharmaceutical firms in 1999 (   1   2 ), was the average amount spent in 1999 above the
average amount spent in 1998? Express H 0 and H 1 two ways, in terms of 1 and  2 , and in terms of  .
b) If 1 was the average grade of traditional university students and  2 was the average grade of nontraditional university students, (   1   2 ), do these differ? Express H 0 and H 1 two ways, in terms of
1 and  2 , and in terms of  .
c) If p1 is the proportion of people who will buy your product after seeing your commercial and p 2 was
the proportion that bought your product before seeing the commercial, ( p  p1  p 2 ), does the
commercial increase the proportion who will buy your product? Express H 0 and H 1 two ways, in terms of
p1 and p 2 , and in terms of p .
d) Have new procedures decreased the variability of delivery times? Two samples have been taken and you
know two sample standard deviations, s1 , taken before the new procedures were instituted, and s 2 , taken
afterwards. Express H 0 and H 1 .
e) If DF  6 and t  1, use the t table to find a range for the p-value in a 2-sided test.
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