252hwk 11/9/07 (Open this document in 'Outline' view!)
Roger Even Bove
HOMEWORK ASSIGNMENTS
Most problems are exercises in the text. ‘text’ means Berenson et. al. – ‘*’ means that problem does not appear or was not used in 8 th
edition. [9th edition numbers are in brackets.](8th edition numbers in parentheses) – ‘*’ means that problem does not appear in 9th
edition, ‘**’ means that the problem is new in the 10th edition. To find these problems go to document 252hwkadd. ) Some problems
are on CD-ROM – this should be in the back of your book. To Get the CD-ROM topics from the website, go to
http://courses.wcupa.edu/rbove/Berenson/CD-ROM%20Topics . The first 7 CD-ROM items are from the 9th edition, the rest are from
the 8th.
Downing and Clark (D&C) is the Barrons paperback. Problems that begin with letters are in the Syllabus Supplement. (Numbers from
2002 – 2003 supplement are in parentheses) (Assignments may be changed - check the website regularly)
A. Parameter Estimation
1. Review of the Normal Distribution
A1
2. Point and Interval Estimation
3. A Confidence Interval for the Mean when the Population Variance is Known.
4. A Confidence Interval for the Mean when the Population Variance is not Known.
A2, text 8.20 (This actually should have been 8.22), 8.50 [8.21, 8.50] (8.21, 8.50) – Answers from both editions will be provided for
8.20[8.21]. 8.96, [8.95] on CD (8.93)
5. Deciding on Sample Size when working with a Mean
A3, 8.38 [8.36] (8.36)
6. A Confidence Interval for a Proportion.
Text 8.24, 8.25, 8.26, 8.58, 8.94 on CD [8.22, 8.23, 8.24, 8.58, 8.93 on CD] (8.22, 8.23, 8.25, 8.58, 8.91a,c)
7. A Confidence Interval for a Variance.
Text 12.1-12.2 [9.72] (9.67), A4
Graded Assignment 1 will be posted.
8. (A Confidence Interval for a Median.)
Optional - A5 -- solution is posted.
B. HYPOTHESIS TESTS FOR ONE SAMPLE
1. The Meaning of Hypothesis Testing
Text 9.1-9.12 [9.1 – 9.12] (9.1 – 9.12), 9.16** [9.17], (9.17)
2. Steps for Testing a Hypothesis Applied to testing for a Population Mean
Text 9.20, 9.28a,c,d, 9.29 a,c,e [9.18, 9.26a,b,d,e, 9.27a,b,d,e], (9.18, 9.26a,b,d,e, 9.27a,b,d,e)
Text 9.48-9.51, 9.59 [9.46 - 9.49, 9.52] (9.44 – 9.47, 9.50)
3. The Use of p-value instead of Significance Levels.
Text 9.28b, 9.29b [9.26c, 9.27c], B7 (B6), Text 9.34-9.44 [9.32 – 9.39, 9.40*, 9.41*, 9.44] (9.26c, 9.27c, B6, 9.32 – 9.39, 9.40)
[9.40* reads ‘Suppose that in a one-tail hypothesis test where you reject H 0 only in the lower tail, you compute the value of the test
statistic z as 1.38, what is the p-value?’ 9.41 reads ‘ In Problem 9.40, what would be your statistical decision if you tested the null
hypothesis at the 0.01 level of significance?’] B8.
Graded Assignment 2 will be posted.
4. Type One and Type Two Errors
Text 9.82-9.86 [9.86 – 9.90] (9.81 – 9.85)
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5. Hypotheses about a Proportion
Text 9.66-9.69, 9.70**, 9.72**[9.62 – 9.64, 9.66*, 9.67*], (9.57 – 9.59)
6. The Sign Test
B1*, B2, B3 (B1, B2)
7. Hypothesis Test for Means - Rare Events
B4, B5 (B3, B4)
8. Hypothesis Tests for a Variance.
Text 12.45[9.80] (9.75), B6 (B5)
C. POWER FUNCTIONS
1. A one-sided Test.
Text 9.75[9.109 on CD] (9.102), C1
2. A Two-Sided Test.
C2
D. COMPARISON OF TWO SAMPLES
1. Two Means, Two Independent Samples, Large Samples.
Text 10.1-10.3, 10.7 [10.1 – 10.3, 10.5] (10.1 – 10.3, 10.5)
2. Two Means, Two Independent Samples, Populations Normally Distributed, Population Variances
Assumed Equal.
Text 10.4, 10.13a, 10.20a, b, e [10.4, 10.15a, 10.13a,b,e]. For the last problem: x1  17.5571, s1  1.9333 , x 2  19.8905 , s 2  4.5767 
(10.4, 10.14, 10.12a,b,e)
3. Two Means, Two independent Samples, Populations Normally Distributed, Population Variances
not Assumed Equal.
Optional Text 10.20[10.13c,d] (10.12c,d) See data above. D3, D4
4. Two Means, Paired Samples (If samples are small, populations should be normally distributed).
Text 10.26, 10.29[10.36, 10.37], D1, D2 (10.32*(in 252hwkadd.), [10.34] (different numbers), 10.25[10.35], D1, D2)
5. Rank Tests.
a. The Wilcoxon-Mann-Whitney Test for Two Independent Samples. Text 12.65[10.48] (10.46)
b. Wilcoxon Signed Rank Test for Paired Samples.
Text 12.74-12.76[10.57-59] (10.80-82 on CD), Downing & Clark 18-15, 18-9 (in chapter 17 in D&C 3rd edition), D5
6. Proportions.
Text 10.32, 10.38, 10.39, 12.32** [12.2, 12.7*, 12.8*] (12.2)
7. Variances.
Text 10.40, 10.43-10.48 [10.16, 10.19 - 10.24, 10.25] (10.15, 10.18 - 10.23, 10.24) D6a (below), D6, D7 (A summary problem), D8
(A summary problem)
Graded assignment 3 will be posted.
E. CHI-SQUARED AND RELATED TESTS.
1. Tests of Homogeneity and Independence
Text 12.18, 12.19 - 21, 12.26 [12.23*, 12.24, 12.27] (12.22, 12.27) E1, E2, E3
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2. Tests of Goodness of Fit
Text 12.51, 12.54 [12.49*, 12.52*. Both on CD12_5], E4, E5, E6
a. Uniform Distribution
b. Poisson Distribution
c. Normal Distribution
3. Kolmogorov-Smirnov Test
E7, E8, E9, E10, E11
a. Kolmogorov-Smirnov One-Sample Test
b. Lilliefors Test.
F. ANALYSIS OF VARIANCE
1. 1-Way Analysis of Variance
Text 11.1-11.6, 11.7**, 11.8 [11.1- 11.7, 11.8*] (11.1- 11.7, 11.8* (Same problem, different numbers – both answers will be posted)
2. 2 -Way Analysis of Variance
Text 11.15-11.18, 11.23, 11.29-11.32, 11.36 [11.15-11.18, 11.23, 11.28-11.30, 11.34] (11.15-11.18, 11.23, 11.28-11.30, 11.34), F1,
F2, F4
3. More than 2-Way analysis of Variance
F3
4. Kruskal-Wallis Test
Text 12.86-12.87, 12.89 [11.39-11.40, 11.42] (11.39-11.40, 11.42), Downing and Clark 18-12, 18-13 (in chapter 17 in D&C 3rd
edition),
5. Friedman Test
Text 12.93-12.95 [11.46-11.48] (11.65-11.67 on CD) Downing and Clark 18-4, 18-6 (in chapter 17 in D&C 3rd edition),
Graded Assignment 4 (Will be posted)
G. LINEAR REGRESSION-Curve Fitting
1. Exact vs. Inexact Relations
2. The Ordinary Least Squares Formula
Text 13.1, 13,2, 13.4 [13.1, 13.3] (13.1, 13.3)
3. Example
4. R 2 , the Coefficient of Determination
H. LINEAR REGRESSION-Simple Regression
1. Fitting a Line
2. The Gauss Markov Theorem
3. Standard Errors
Text 13.11, 13.12, 13.16[13.9, 13.10, 13.14] (13.9, 13.10, 13.14)
4. The Variance of a and b.
I. LINEAR REGRESSION-Confidence Intervals and Tests
1. Confidence Intervals for b1 .
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2. Tests for b1 .
3. Confidence Intervals and Tests for b0
Text 13.40-13.42, 13.49 [13.35-13.37, 13.43] (13.35-13.37, 13.43) (In 13.42[13.37] do test for b0 as well)
4. Prediction and Confidence Intervals for y
Text 13.55-13.56, 13.58 [13.49-13.51] (13.47-13.49)
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J. MULTIPLE REGRESSION
1. Two explanatory variables
a. Model
b. Solution.
2. Interpretation
Text 14.1, 14.3, 14.4 [14.1, 14.3, 14.4] (14.1, 14.3, 14.4) Minitab output for 14.4 will be available on the website; you must be able to
answer the problem from it.
3. Standard errors
J1, Text Problems 14.9, 14.14, 14.23, 14.26 [14.13, 14.16, 14.20, 14.23] (14.17, 14.19, 14.24, 14.27)
4. Stepwise regression
Problem J2 (J1), Text exercises 14.32, 14.34[14.28, 14.29] (14.32, 14.33)
(Computer Problem – instructions to be given),
K. REGRESSION EXTENSIONS
1. Residual Analysis
Text 13.23, 13.24, 13.26, 14.18 [13.20, 13.21, 13.22, 14.9] (13.20, 13.21, 13.22, 14.9)
2. Dummy Variables
14.38-14.39, 14.41 [14.33 – 14.35] (15.6 – 15.8)
3. Nonlinear regression
15.1, 15.6, 15.7 [15.1, 15.6, 15.7] (15.1, 15.13, 15.14)
4. Runs test
K1
5. Durbin-Watson test
13.32-13.34 [13.28, 13.29, 13.30] (13.28, 13.29, 13.30)
L. CORRELATION
1. Simple Correlation
2. Correlation when x and y are both independent
Problem L1, Text 13.41[13.36] (Compute correlation and test correlation for significance!)
3. Tests of Association
Problem L3, L2 (L1, L2)
4. Multiple Correlation
5. Partial Correlation
6. Collinearity
Text 15.18-15.20 [15.16-15.18] (15.19-15.21) (A printout will be supplied for the last problem – make sure that you understand it.)
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Appendix - 1999 last computer problem and 2000 graded assignments.
1999 Last Computer Problem
(The problem was 11.26 in the 8th 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
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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’ 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.
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
6
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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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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 non-traditional 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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