Download Exercises for Lecture 22 – Stat 112

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Exercises for Lecture 22 – Stat 112
1. Moore and McCabe, third edition, 12.9 (do 12.1 instead in fourth edition).
2. (based on Moore and McCabe, third edition, 12.5 and 12.6 (12.18 and 12.19 in fourth
edition)
Do piano lessons improve the spatial-temporal reasoning of preschool children? In
exercise 7.51 (Exercise 7.65) in fourth edition, this questions was examined by
comparing the change scores (after treatment minus before treatment) of 34 children who
took piano lessons with the scores of 44 children who did not. The latter group actually
contained three groups of children: 10 were given singing lessons, 20 had some computer
instruction and 14 received no extra lessons. The data appears in Moore and McCabe and
is in piano.JMP.
(a) The following is the output for the multiple linear regression of score on a dummy
variable for piano, a dummy variable for singing and a dummy variable for computer.
Analyze the question of whether there is any difference between the spatial-temporal
reasoning of children who receive piano lessons, singing lessons, computer instruction
and no extra lessons. State the null and alternative hypotheses, the test statistic with
degrees of freedom, the P-value and your conclusion.
Response Scores
Whole Model
Actual by Predicted Plot
Scores Actual
10
5
0
-5
-5
0
5
10
Scores Predicted P<.0001 RSq=0.27
RMSE=2.7348
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.272481
0.242987
2.734753
1.794872
78
Analysis of Variance
Source
Model
Error
C. Total
DF
3
74
77
Sum of Squares
207.28139
553.43655
760.71795
Mean Square
69.0938
7.4789
F Ratio
9.2385
Prob > F
<.0001
Parameter Estimates
Term
Intercept
Estimate
0.7857143
Std Error
0.730893
t Ratio
1.08
Prob>|t|
0.2859
Term
Piano
Singing
Computer
Estimate
2.8319328
-1.085714
-0.335714
Std Error
0.868431
1.132295
0.952968
t Ratio
3.26
-0.96
-0.35
Prob>|t|
0.0017
0.3408
0.7256
Effect Tests
Source
Piano
Singing
Computer
Nparm
1
1
1
DF
1
1
1
Sum of Squares
79.530112
6.876190
0.928151
F Ratio
10.6340
0.9194
0.1241
Prob > F
0.0017
0.3408
0.7256
Residual by Predicted Plot
8
Scores Residual
6
4
2
0
-2
-4
-6
-8
-5
0
5
10
Scores Predicted
(b) Use the Bonferroni multiple comparisons procedure to compare the group means.
The pooled estimate of the standard deviation is s p  2.7348 . The four group means are
Group
Piano
Singing
Computer
None
Mean
3.618
-0.300
0.450
0.786
Number in Group
34
10
20
14
3. Moore and McCabe, question 12.11 (12.30 in fourth edition). The data is in
insect.JMP.
4.
New chemicals are screened to see if they cause cancer in lab mice. A
“bioassay” can be done with 500 mice; 250 are chosen at random and given the
test chemical in their food; 250 get a normal lab diet. After 33 months, cancer
rates in the two groups are compared, using the two sample z-test.
Investigators look at cancer rates in about 25 organs and organ systems – lungs, liver,
circulatory system, etc. With one chemical, z  1.8 for the lungs, z  2.4 for the liver,
z  2.1 for leukemia, and there are another 22 values of z that range from –1.6 to 1.5.
The investigators conclude that the chemical causes liver cancer ( z  2.4, the p-value for
the one-sided test is approximately 0.01). Comment briefly on whether you think the
investigators conclusion is appropriate.
5. What is the distinction between a planned and an unplanned comparison?