4/12/01 252x0131
(Page layout view!)
ECO252 QBA2
THIRD HOUR EXAM
April 17, 2001
Name
Hour of Class Registered (Circle)
MWF TR 10 12 12:30 2:00
I. (10+ points) Do all the following;
1. Hand in your computer printouts for problems 2 and 3.(5 points – 3 point penalty for not handing in). remember that the ANOVA printout must be completed, using a 5% significance level, for full credit. I should be able to tell what is tested and what are the conclusions.
2. Do not do the following unless you handed in at least two outputs.
On the next few pages there are problems very much like the ones you did. a. A random survey of CEOs (Don Black) asks the question "Do you agree that an increase of market share is a reason to consider a merger?" Responses (Agree?) were between 5 and 1, with 5 indicating strong agreement. Responses were classified in 2 ways, with 'years' dividing respondents according to the number of years they had been with the company and 'size' dividing firms according to the companies' sales in millions of dollars. The output follows.
Tabulated Statistics
ROWS: Size COLUMNS: Years
1 2 3 ALL
1 4 4 4 12
2 4 4 4 12
3 4 4 4 12
4 4 4 4 12
ALL 16 16 16 48
CELL CONTENTS --
COUNT
Tabulated Statistics
ROWS: Size COLUMNS: Years
1 2 3
1 2.0000 2.0000 2.0000
3.0000 1.0000 1.0000
2.0000 2.0000 1.0000
2.0000 3.0000 2.0000
2 2.0000 2.0000 2.0000
1.0000 3.0000 3.0000
2.0000 2.0000 1.0000
3.0000 3.0000 2.0000
3 3.0000 3.0000 3.0000
4.0000 2.0000 2.0000
4.0000 4.0000 3.0000
5.0000 4.0000 3.0000
4 3.0000 3.0000 2.0000
4.0000 3.0000 3.0000
4.0000 3.0000 2.0000
3.0000 4.0000 3.0000

4/12/01 252x0131
CELL CONTENTS --
Agree?:DATA
Tabulated Statistics
ROWS: Size COLUMNS: Years
1 2 3 ALL
1 2.2500 2.0000 1.5000 1.9167
2 2.0000 2.5000 2.0000 2.1667
3 4.0000 3.2500 2.7500 3.3333
4 3.5000 3.2500 2.5000 3.0833
ALL 2.9375 2.7500 2.1875 2.6250
CELL CONTENTS --
Agree?:MEAN
MTB > Twoway c1 c2 c3;
SUBC> Means c2 c3.
Two-way Analysis of Variance
Analysis of Variance for Agree?
Source DF SS MS
Size 3 17.083 5.694
Years 2 4.875 2.437
Interaction 6 2.292 0.382
Error 36 17.000 0.472
Total 47 41.250
Individual 95% CI
Size Mean -----+---------+---------+---------+------
1 1.92 (------*------)
2 2.17 (------*------)
3 3.33 (------*-----)
4 3.08 (-----*------)
-----+---------+---------+---------+------
1.80 2.40 3.00 3.60
Individual 95% CI
Years Mean --------+---------+---------+---------+---
1 2.94 (---------*---------)
2 2.75 (---------*---------)
3 2.19 (---------*--------)
--------+---------+---------+---------+---
2.10 2.45 2.80 3.15
(i) Complete the ANOVA table that compares the effect of size and years on the response of the CEOs. (2)
(ii) Is there a statistically significant difference between the means for responses of CEOs with different years of service? Show what numbers brought you to your conclusion. (2)
2

4/12/01 252x01321 b. Ken Black says that the Delta Wire Corporation believes that the more positive outlook created by employee education sessions results in greater interest in the job, and thus fewer sick days per worker. A random sample of workers is taken, and a regression is run with 'sick' (number of sick days per worker) as the dependent variable and 'educ' (number of hours of employee education) as the independent variable.
Part of the output appears below.
Regression Analysis
The regression equation is
Sick = 7.92 - 0.0864 Educ
Predictor Coef Stdev t-ratio p
Constant 7.9197 0.7837 10.11 0.000
Educ -0.08637 0.01574 -5.49 0.000 s = 2.368 R-sq = 62.6% R-sq(adj) = 60.5%
Analysis of Variance
SOURCE DF SS MS F p
Regression 1 168.80 168.80 30.10 0.000
Error 18 100.95 5.61
Total 19 269.75
Unusual Observations
Obs. Educ Sick Fit Stdev.Fit Residual St.Resid
4 120 1.000 -2.444 1.414 3.444 1.81 X
10
5
0
0 50
Educ
100
(i) What equation does it give to relate education hours to number of sick days? How many sick days does it predict that someone with 10 hours of education will take? (2)
(ii) What test or tests would lead you to believe that the company is correct? Cite evidence using a 5% significance level.
3

4/12/01 252x0131
II. Do at least 4 of the following 5 Problems (at least 10 each) (or do sections adding to at least 40 points -
Anything extra you do helps, and grades wrap around) . Show your work! State H
0
and H
1 where applicable. Never say 'yes' or 'no' without a statistical test.
1. a. In the ANOVA problem beginning on page 1, there is a plot for an individual 95% confidence interval for the mean for size 3.
(i) Figure out, using your formulas and the data on the pages, what this interval actually is. (2)
(ii) Is there a significant difference between the means for level 1 and level 2 of 'years?
To answer this question, do 95% confidence intervals for the difference between these two means that are (

) Valid when used alone. (1) (

) Valid when used with other possible differences between means. (2) and state a conclusion (1) b. In the regression problem on page 3.
(i) Add a regression line to the graph (1)
(ii) Do a 99% confidence interval for the slope of the equation. (2)
(iii) Find s
2 e
from the printout and (if the sample mean for x is 36.70 and the sample standard deviation for x is 34.51) do a confidence interval for the mean number of sick days taken by someone with 10 hours of education (4).
4

4/12/01 252x0131
2. According to Ken Black an agricultural researcher planted parts of six blocks of land with peanuts , using each of three different methods.. Part of the results are given below. Data is yield per acre in thousands.
Assume that the parent distribution is Normal and compare the mean yields for the three methods noting the fact that it is cross-classified. Use
 
.
01 .
Note: If you wish to ignore that the fact that the data is blocked, indicate this now and compare the column means assuming that the data is three independent random samples from a normal distribution.(10). (
 
.
01 )
3
4
5
6
BLOCK
1
2
Method 1
1.31
1.27
1.28
1.22
1.19
1.30
Sum 7.57
Sum of squares 9.5619
Method 2
1.08
1.10
1.05
1.02
0.99
0.95
6.19
6.4019
Method 3
0.85
1.02
0.78
0.87
0.80
0.96
?
?
Sum
3.24
3.39
3.11
3.11
2.98
3.21
Sum of Squares
3.6050
3.8633
3.3493
3.2857
3.0362
?
5

4/12/01 252x0131
3. a. Data from problem 2 is repeated below. Assume that the distribution is not normal, but
BLOCK that it is blocked (cross-classified), and again compare the distributions represented by the columns. (5) (
 
.
01 )
Method 1 Method 2 Method 3 Sum Sum of Squares
4
5
6
1
2
3
1.31
1.27
1.28
1.22
1.19
1.30
1.08
1.10
1.05
1.02
0.99
0.95
0.85
1.02
0.78
0.87
0.80
0.96
3.24
3.39
3.11
3.11
2.98
3.21
3.6050
3.8633
3.3493
3.2857
3.0362
?
Sum 7.57
Sum of squares 9.5619
6.19
6.4019
?
? b. A researcher looks at the effect of industry (Factor A) and size (measured by $millions in sales)
(Factor B) on Research and Development expenditures as a per cent of sales. A sample is taken of 4 firms in each industry-size category. The sample is repeated over three different years (Factor C). If the researcher looks at 3 size categories within 5 industries over the three years, generate an ANOVA table showing all possible interactions, using the following data. SSA = 24.021, SSB = 4.829, SSC = 4.029, SSAB = 9.059,
SSAC = 14.976, SSBC = 2.528, SSABC = 9.615, SST = 150.672. Using a 5% significance level, explain whether the size of the firm and the industry seem to make a difference in R&D expenditures. Which of the other differences and interactions are significant.? (7)
6

4/12/01 252x01321
4. (Levine et. al. p 839) The following data are charges in dollars per minute and billions of minutes of calls made to 9 countries from the US in 1996.
Country minutes charge
Canada 3.05 0.34
Britain 1.02 0.73
Germany 0.66 0.88
Japan 0.57 1.00
Dom.Rep. 0.41 0.84
France 0.36 0.81
India 0.29 1.38
Brazil 0.28 0.96
Taiwan 0.27 0.97
For your convenience the following values are given:
 x

7.91,
 x
2 
7.5515, a. Compute the regression equation
 y

Y
  b
0
 b x
6.91,
 y
2 
11.6365 and n

9 .
to predict billions of minutes of calls. (6) b. On the basis of your regression, how many billions of minutes of calls do you expect when the charge is
$.90 ? (1) c. Compute R
2
. (4) d. Compute s e
. (3) e. Compute s b
1
and do a significance test on b
1
.(4) f.. Do a prediction interval for billions of minutes of calls when the charge is $.90 (3) g. Using your SST etc., put together the ANOVA table (6)
7

4/12/01 252x0131
(Intentionally left blank for calculations)
8

4/12/01 252x01321
5. The failure times in thousands of hours are given for a random sample of 7 components.
0.5 8.5 7.8 8.3 4.7 3.5 4.4
Minitab says that the sample mean is 5.39 and the sample standard deviation is 2.97
Use methods appropriate to testing goodness of fit. a. Test the hypothesis that these numbers came from a normal distribution. Use a 5% significance level. (5) b. Test the hypothesis that the above data came from a normal distribution with a mean of 4.5 and a standard deviation of 2 (5) c. A television set distributorship believes that television ownership in the local area is distributed according to a Poisson distribution with a mean of 4. A sample of 100 is taken. Is this true? Use a 5% significance level. (5)
Number of TV sets: 0 1 2 3 4 5 6 or more.
Number of Households: 2 30 30 18 10 2 8
9