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ASSIGNMENT Chapter 11
Statistical Methods
NAME:
M&S 575, 577, 589, 600, 608, 616
11.23 (4 points) Redshifts of Quasi Stellar Objects. Astronomers call a shift in the
spectrum of galaxies a “redshift.” A correlation between redshift level and apparent
magnitude (i.e., brightness on a logarithmic scale) of a quasi-stellar object was
discovered and reported in the Journal of Astrophysics & Astronomy (Mar./Jun. 2003).
Physicist D. Basu (Carleton University, Ottawa) applied simple linear regression to data
collected for a sample of over 6,000 quasi-stellar objects with confirmed redshifts. The
analysis yielded the following results for a specific range of magnitudes: y = 18.13+
6.21x, where y = magnitude and x = redshift level.
a. Graph the least squares lines. Is the slope of the line positive or negative?
ANSWER

b. Interpret the estimate of the y-intercept in the words of the problem.
ANSWER
c. Interpret the estimate of the slope in the words of the problem.
ANSWER
11.28 (4 points) Sweetness of orange juice. The quality of the orange juice produced by
a manufacturer is constantly monitored. There are numerous sensory and chemical
components that combine to make the best-testing orange juice. For example, one
manufacturer has developed a quantitative index of the “sweetness” of orange juice. (The
higher the index, the sweeter is the juice.) Is there a relationship between the sweetness
index and a chemical measure such as the amount of water-soluble pectin (parts per
million) in the orange juice? Data collected on these two variables during 24 production
runs at a juice-manufacturing plant are shown in the table. Suppose a manufacturer wants
to use simple linear regression to predict the sweetness (y) from the amount of pectin (x).
OJUICE
Run
Sweetness Index
Pectin (ppm)
1
5.2
220
2
5.5
227
3
6.0
259
4
5.9
5
5.8
6
6.0
7
5.8
8
5.6
9
5.6
10
5.9
11
5.4
12
5.6
13
5.8
14
5.5
15
5.3
16
5.3
17
5.7
18
5.5
19
5.7
20
5.3
21
5.9
22
5.8
23
5.8
24
5.9
a. Find the least squared line for the data.
ANSWER
210
224
215
231
268
239
212
410
256
306
259
284
383
271
264
227
263
232
220
246
241
b. Interpret 0 and 1 in the words of the problem.
ANSWER
c. 
Predict
the sweetness index if the amount of pectin in the orange juice is 300
ppm. [Note: A measure of reliability of such a prediction is discussed in Section
11.6.]
ANSWER
11.63 (3 points) Relation of eye and head movements. How do eye and head
movements relate to body movements when a person reacts to a visual stimulus?
Scientists at the California Institute of Technology designed an experiment to answer this
question and reported their results in Nature (Aug 1998). Adult male rhesus monkeys
were exposed to a visual stimulus (i.e., a panel of light-emitting diodes), and their eye,
head, and body movements were electronically recorded. In one variation of the
experiment, two variables were measured: active head movement (x, percent per degree)
and body-plus-head rotation (y, percent per degree). The data for n = 39 trials were
subjected to a simple linear regression analysis, with the following result: 1 = .88,
s = .14
1

a. Conduct a test to determine whether the two variables, active head movement x
and body-plus-head rotation y are positively linearly related.
 Use  = .05.
ANSWER
b. Construct and interpret a 90% confidence interval for 
1 .
ANSWER
c. The scientists want to know whether the trueslope of the line differs
significantly from 1. On the basis of your answer to part b, make the appropriate
inference.
ANSWER
1.80 (6 points) Salary linked to height. Are short people shortchanged when it comes to
salary? According to business professors T. A. Judge (University of Florida) and D. M.
Cable (University of North Carolina), tall people tend to earn more money over their
career than short people earn. (Journal of Applied Psychology, June 2004.) Using data
collected from participants in the National Longitudinal Surveys begun in 1979, the
researchers computed the correlation between average earnings (in dollars) from 1985 to
2000 and height (in inches) for several occupations. The results are given in the following
table:
Occupation
Sales
Managers
Blue Collar
Service Workers
Professional/Technical
Clerical
Crafts/Forepersons
Correlation, r
Sample Size, n
.41
.35
.32
.31
.30
.25
.24
117
455
349
265
453
358
250
a. Interpret the value of r for people in sales occupations.
ANSWER
b. Compute r2 for people in sales occupations. Interpret the result.
ANSWER
c. Given H0 and Ha for testing whether average earnings and height are positively
correlated.
ANSWER
d. The test statistic for testing H0 and Ha in part c is t =
r n 2
1 r 2
. Compute the
value of t for people in sales occupations.
ANSWER

e. Use the result you obtained in part d to conduct the test at  = .01. State the
appropriate conclusion.
ANSWER

11.98 (2 points) Sweetness of orange juice. Refer to the simple linear, regression of
sweetness index y and amount of pectin, x, for n = 24 orange juice samples, presented in
Exercise 11.28 (p. 577). The SPSS printout of the analysis is shown below. A 90%
confidence interval for the mean sweetness index E(y) for each value of x is shown on the
SPSS spreadsheet. Select an observation and interpret this interval.
run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
ANSWER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
sweet
5.2
5.5
6.0
5.9
5.8
6.0
5.8
5.6
5.6
5.9
5.4
5.6
5.8
5.5
5.3
5.3
5.7
5.5
5.7
5.3
5.9
5.8
5.8
5.9
pectin
220
227
259
210
224
215
231
268
239
212
410
256
306
259
284
383
271
264
227
263
232
220
246
241
lower90m
5.64898
5.63898
5.57819
5.66194
5.64337
5.65564
5.63284
5.55553
5.61947
5.65946
5.05526
5.58517
5.43785
5.57819
5.50957
5.15725
5.54743
5.56591
5.63898
5.56843
5.63125
5.64898
5.60640
5.61587
upper90m
5.83848
5.81613
5.72904
5.87173
5.82560
5.85493
5.80379
5.71011
5.78019
5.86497
5.55416
5.73592
5.65219
5.72904
5.68213
5.57694
5.70434
5.71821
5.81613
5.72031
5.80075
5.83848
5.76091
5.77454
11.112 (4 points) Predicting sale prices of homes. Real-estate investors, home buyers,
and homeowners often use the appraised value of property as a basis for predicting the
sale of that property. Data on sale prices and total appraised value of 78 residential
properties sold in 2006 in an upscale Tampa, Florida, neighborhood named Hunter's
Green are saved in the HUNGREEN file. Selected observations are listed in the
following table.
HUNGREEN (selected observations)
Property
Sale Price
Appraised Value
1
$489,900
$418,601
2
1,825,000
1,577,919
3
890,000
687,836
4
250,00
191,620
5
1,275,000
1,063,901
:
:
:
74
325,000
292,702
75
516,000
407,449
76
309,300
272,275
77
370,000
347,320
78
580,000
511,359
a. Propose a straight-line model to relate the appraised property value (x) to the
sale price (y) for residential properties in this neighborhood.
ANSWER
b. A MNITAB scatterplot of the data with the least squared lines is shown (p.
616, top). Does it appear that a straight-line model will be an appropriate fit to the
data?
ANSWER
c. A MINITAB simple linear regression printout is also shown (p. 616, bottom).
Find the equation of the least squared line. Interpret the estimated slop and yinterpret in the words of the problem.
ANSWER
Total points: 23