Exam 4 Fall02
1.
How many hormone types are compared?
(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
2.
Which of the following is the point estimate for

, the true overall average growth?
(a) 11.50
(b) 12.75
(c) 13.90
(d) 15.30
(e) 17.50
3.
Which of the following null hypothesis would you use to investigate if the true average growth depend on the choice of hormone? (I am asking if there are any differences between them)
(a) H
0
:

1
 
2
(b)
(c)
(d)
H
0
H
0
H
0
:
:
:
:
1
2

1
 
1



2

2


1

4

1


5
(

2
 
1
3
 

3
 
4
3
 
3
 
4




4

5


5
)

5

(e) H
0
4.
Which of the following null hypothesis would you use to investigate if the true average growth applying hormone 1 different than the others?
(a) H
0
:

1
 
2
(b)
(c)
(d)
H
0
H
0
H
0
:
:
:
:
1
2

1
 
1



2

2


1

4

1


5
(

2


1
3
 

3
 
4
3
 
3
 
4




4

5


5
)

5

(e) H
0
5.
Which of the following is the point estimate for

2
-

1
(the difference between the true average growth applying hormone 2 and hormone 1)
(a) –4.75
(b) –5
(c) 1.25
(d) 4.75
(e) 5
6.
If the true standard deviation of growth is assumed to be the same applying hormone types 1 and 2, the 95% confidence interval on the difference in true average growth applying hormone 1 and hormone
2 is (-11.7568 , 1.7568). Which of the following would be the interpretation?
(a) The true average growth applying hormone 1 and 2 are different
(b) The true average growth does depend on the choice of the hormone
(c) The true average growth applying hormone 1 and 2 are not different
(d) The true average growth does not depend on the choice of the hormone

Exam 4 Fall02
7.
If the true standard deviation were assumed to be the same applying hormone types 1 and 2, which of the following test statistics would you use to investigate if the true average growth applying hormone 1 and 2 are different?
(a) –3.49
(b) -1.811
(c) 1.811
(d) 1.868
(e) 3.49
8.
Is the assumption of equal true variances applying hormone 1 and 2 are correct using the significance level of 0.05? (p-value is based on the given test statistics for each choice)
(a) Yes, the test statistics is 1.167 and the corresponding P-value is 0.7288
(b) No, the test statistics is 1.167 and the corresponding P-value is 0.7288
(c) Yes, the test statistics is 1.361 and the corresponding P-value is 0.5878
(d) No, the test statistics is 1.361 and the corresponding P-value is 0.5878
(e) Yes, the test statistics is 1.66 and the corresponding P-value is 0.798
9.
Is the assumption of equal true variances of growth using all hormone types correct using the significance level of 0.05?
(a) Yes, the test statistics is 1.167 and the corresponding P-value is 0.7288
(b) No, the test statistics is 1.167 and the corresponding P-value is 0.7288
(c) Yes, the test statistics is 1.361 and the corresponding P-value is 0.5878
(d) No, the test statistics is 1.361 and the corresponding P-value is 0.5878
(e) Yes, the test statistics is 1.66 and the corresponding P-value is 0.798
10.
What is the point estimate for the constant standard deviation when you investigate if the true average growth depend on the choice of hormone?
(a) 3.795
(b) 14.400
(c) 50.100
(d) 207.360
(e) 215.500
11.
In testing H
0
: p
1
 p
2
, the null hypothesis must be rejected in one of the following outcomes. For what result must you reject H ? (Use

=0.01 and assume you have a large sample. Possible table
0 values you may need are z
0.02
=2.05, z
0.01
=2.33, z
0.005
=2.575).
(a) z=2.53
(b) z=2.31
(c) I need to use t distribution here but critical values are not given
(d) z=-2.31
(e) z=-2.53
12.
Regress time on strength. Which of the following is the least squares regression line?
(a) Time = -8.78 + 18.8735

Strength
(b) Strength = -8.78 + 18.8735

Time
(c) Time = 18.8735 - 8.78

Strength
(d) Strength = 18.8735 - 8.78

Time
(e) I do not have enough information to compute it.

Exam 4 Fall02
13.
What is the predicted time when the strength was 12.5?
(a) -90.88
(b) 102.05
(c) 227.14
(d) 12.5 is not in the range of strength to compute it
(e) 12.5 is not in the range of time to compute it
14.
What is the average change in time when the strength is increased by 0.1 unit?
(a) 0.878
(b) 1.88735
(c) 8.78
(d) 18.8735
(e) I cannot compute it since 0.1 is not in the range of strength
15.
Which of the following is the possible relation between time and strength in general?
(a) They are positively related
(b) They are negatively related
(c) They are not related
16.
I am not sure if time is really related with strength in general. Which of the following null hypothesis would you use to test this?
(a) H
0
:

0
 
8 .
78
(b)
(c)
H
H
0
0
:
:

1

0


18 .
8735
0
(d)
(e)
H
H
0
0
:
:

1

0


0

8 .
78 and H
0
:

1

18 .
8735
17.
Which of the following is the Pearson’s correlation coefficient between time and strength?
(a) -0.98995
(b) -0.97800
(c) 0.97800
(d) 0.98000
(e) 0.98995
18.
Which of the following is the point estimate for the constant standard deviation for residuals?
(a) 16.62
(b) 49.86
(c) 276
(d) 352.37
(e) 124163
19.
Which of the following is the corresponding residual when the strength is 19?
(a) –19.1835
(b) –17.1835
(c) I do not have enough information to compute it.
(d) 17.1835
(e) 19.1835
20.
If I claim that

1

19 , do I have enough evidence based on the data using

=0.05 to prove that I am right? (note that the critical value for this test is 2.262)
(a) Yes
(b) No

Exam 4 Fall02
21.
I decided to take the square root of time (called it sqrttime) and regress sqrttime on strength. I called this as Model 2 where as the first one was Model 1. The R 2 computed is 94% with model 2. Which of those models would you use?
(a) Model 1
(b) Model 2
(c)
I do not know first model’s R 2 to make a comparison.
The data on plant growth after the application of different types of growth hormone is recorded.
Hormone 1
Hormone 2
Hormone 3
Hormone 4
Hormone 5
13
21
18
7
6
17
14
15
11
11
7
20
20
18
15
14
17
17
10
8
We are trying to investigate if choice of hormone is important for the plant growth. We modeled the data using the single factor ANOVA, X ij
  i
  ij
where i=1,...,5 and j=1,...,4.
X : plant growth ij
 i
: true average plant growth for i th hormone type.

 ij
 i
5 

1
 i
/ 5 : the true overall average plant growth
: errors which are normally distributed with mean, 0 and the constant variance,

2
.
The following output is obtained using the statistical software MINITAB.
Analysis of Variance
Source DF SS MS F P
Factor 4 200.3 50.1 3.49 0.033
Error 15 215.5 14.4
Total 19 415.8
Level N Mean StDev
Hormone1 4 12.750 4.193
Hormone2 4 17.750 3.594
Hormone3 4 17.500 2.082
Hormone4 4 11.500 4.655
Hormone5 4 10.000 3.916
Bartlett's Test (normal distribution)
Test Statistic: 1.660
P-Value : 0.798
Levene's Test (any continuous distribution)
Test Statistic: 0.283
P-Value : 0.884

Exam 4 Fall02
ML Estimates - 95% CI
99
95
90
80
70
60
50
40
30
20
10
5
ML Estimates
Mean 13.9
StDev 4.55961
Goodness of Fit
AD* 0.874
1
0 10 20
An experiment to measure the macroscopic magnetic relaxation time in crystals as a function of the strength of the external biasing magnetic field yielded the following data.
Strength 11
Time 187
12.5 15.2 17.2 19
225 305 318 367
20.8 22
365 400
24.2 25.3 27
435 450 506
29
558
Simple linear regression, Y
 
0
 
1 x
 e is used modeling this data. The parameters

0
and

1
are true values of intercept and slope. Regressing relaxation time on strength, we obtained the following output using MINITAB software.
Predictor Coef SE Coef T P
Constant -8.78 18.75 -0.47 0.651 strength 18.8735 0.8902 21.20 0.000
S = 16.62 R-Sq = 98.0% R-Sq(adj) = 97.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 124163 124163 449.47 0.000
Residual Error 9 2486 276
Total 10 126650
Answer Key:
1.D 2.C 3.C 4.E 5.E 6.C 7.B 8.C 9.E 10.A 11.A 12.A
13.C 14.B 15.A 16.D 17.E 18.A 19.D 20.A 21.A