15.3
13.1
15.2
15.9
15.1
14.9
13.6
13.7
15.3
15.5
14.5
16.5
13.4
15.2
15.3
13.8
14.3
12.6
15.3
14.8
14.1
14.4
14.3
15.6
14.8
14.6
15.6
15.1
14.8
15.2
15.6
14.5
15.2
14.3
15.8
17.0
14.3
14.6
16.1
12.8
14.5
15.4
13.3
14.9
14.3
16.4
13.9
16.1
14.6
15.2
14.1
14.8
16.4
14.2
15.2
16.6
14.1
16.8
15.4
14.0
16.9
15.7
14.4
15.6
Construct normal probability plots for two groups of the data: the first 40 observations (the first
4 columns) and the last 40 observations. Construct both plots on the same axes. What tentative
conclusions can you draw?
Both sets of data appear ____ normally distributed and with roughly the same ____ value. The
difference in slopes for the two lines indicates that a change in ____ might have occurred. This
could have been the result of a change in processing conditions, the quality of the raw material or
some other factor.
SOLUTION
Reserve Supplemental Exercises Chapter 6 Problem 8
The following data are the temperatures of effluent at discharge from a sewage treatment facility
on consecutive days:
43
47
51
48
52
50
46
49
45
52
46
51
44
49
46
51
49
45
44
50
48
50
49
50
Construct a normal probability plot of the data. Based on the plot, what tentative conclusions can
you draw?
A normal distribution is _____ for these data. There _____ repeated values in the data so the plot
_____ off the line.
SOLUTION
Reserve Supplemental Exercises Chapter 6 Problem 9
The “cold start ignition time” of an automobile engine is being investigated by a gasoline
manufacturer. The following times (in seconds) were obtained for a test vehicle: 1.75, 1.92, 2.62,
2.35, 3.09, 3.15, 2.53, 1.91. A second formulation of the gasoline was tested in the same vehicle,
with the following times (in seconds): 1.83, 1.99, 3.13, 3.29, 2.65, 2.87, 3.40, 2.46, 1.89, and
3.35. Construct normal probability plots of the cold start ignition time data. Construct a separate
plot for each gasoline formulation, but arrange the plots on the same axes. What tentative
conclusions can you draw?
Although we do not have sufficient data points to really see a pattern, there seem to ____
significant deviations from normality for either sample. The ____ difference in slopes indicates
that the _____ of the populations are very _______.
SOLUTION
Reserve Supplemental Exercises Chapter 6 Problem 10
The United States Golf Association tests golf balls to ensure that they conform to the rules of
golf. Balls are tested for weight, diameter, roundness, and overall distance. The overall distance
test is conducted by hitting balls with a driver swung by a mechanical device nicknamed “Iron
Byron” after the legendary great Byron Nelson, whose swing the machine is said to emulate.
Following are 100 distances (in yards) achieved by a particular brand of golf ball in the overall
distance test.
261.3
259.4
265.7
270.6
274.2
254.5
283.7
258.1
270.5
255.1
268.9
267.4
234.3
263.2
254.2
270.7
233.7
263.5
244.5
259.5
257.5
257.7
272.6
253.7
262.2
252.0
274.9
233.7
237.9
274.0
264.5
244.8
264.0
272.1
260.2
255.8
260.7
245.5
279.6
237.8
273.3
263.7
241.4
260.6
280.3
272.7
261.0
279.3
252.1
244.3
272.2
248.3
278.7
236.0
279.8
245.6
241.2
251.1
267.0
273.4
247.7
272.8
270.5
254.4
232.1
271.5
242.9
273.6
251.6
256.8
273.0
240.8
276.6
264.5
226.8
255.3
266.6
250.2
255.8
285.3
240.5
255.0
273.2
251.4
276.1
277.8
268.5
Use the data above to calculate the descriptive statistics for the yardage distance.
Construct a box plot of the yardage distance and complete the interpretation of the plot. How
does the box plot compare in interpretive value to the original stem-and-leaf diagram?
The plot indicates that most balls (between first and third quartiles) will fall somewhere in the
range from ____ to _____. This type of information _____ be obtained from the stem-and-leaf
graph.
SOLUTION
Sample mean
x
=
260.3
Sample standard deviation
=
13.4
Reserve Supplemental Exercises Chapter 6 Problem 11
Patients arriving at a hospital emergency department present a variety of symptoms and
complaints. The following data were collected during one weekend night shift (11:00 p.m. to
7:00 a.m.):
Chest pain
8
Difficulty breathing
7
Numbness in extremities
3
Broken bones
11
Abrasions
16
Cuts
21
Stab wounds
9
Gunshot wounds
4
Blunt force trauma
10
Fainting, loss of consciousness
4
Other
10
Calculate the numerical summaries of these data and fill the table.
SOLUTION
Sort the categories by the number of instances in each category. Bars are used to indicate the counts and this sorted bar chart is known as a Pareto chart
(discussed in Chapter 15).
Cuts
Abrasions
Broken
bones
Blunt force
trauma
Other
Stab
wounds
Chest
pain
Difficulty
breathing
Fainting, loss of
conciousness
Gunshot
wounds
Numbness in
extremities
Frequency
21
16
11
10
10
9
8
7
4
4
3
Percent
10.7
9.7
8.7
6.8
Reserve Supplemental Exercises Chapter 6 Problem 12
The force needed to remove the cap from a medicine bottle is an important feature of the product
because requiring too much force may cause difficulty for elderly patients or patients with
arthritis or similar conditions. The data below presents the results of testing a sample of 68 caps
attached to bottles for the force (in pounds) required for removing the cap.
14
18
27
24
24
28
22
21
16
17
22
16
16
18
30
16
14
15
25
15
16
15
15
19
19
10
22
17
15
17
20
17
20
15
17
20
24
27
17
32
31
27
21
21
26
31
34
32
24
16
37
36
34
20
19
21
14
14
19
15
30
24
15
17
17
21
34
24
Stem-and-leaf of Force N = 68
Leaf Unit = 1.0
1
1
0
1
1
13
1
444455555555
27
1
66666677777777
33
1
889999
(9)
2
000011111
26
2
222
23
2
4444445
16
2
6777
12
2
8
11
3
0011
7
3
22
5
3
444
2
3
67
What are the average and the standard deviation of the force?
The average is ____ and the sample standard deviation is _____.
Comment on the normal probability plot of the data.
There is a number of _________ values for force that are seen as points stacked vertically on the
plot. This is probably due to rounding of the force value to two digits. There are _______ lower
force values than are expected from a normal distribution.
If the upper specification on required force is 30 pounds, what proportion of the caps do not meet
this requirement? Round your answer to three decimal places (eg. 98.765).
What proportion of the caps exceeds the average force plus 2 standard deviations? Round your
answer to three decimal places (eg. 98.765).
Suppose that the first 36 observations in the table come from one machine and the remaining
come from a second machine (read across the rows and the down). Construct box plots of the
data and calculate the descriptive statistics for two groups of observations. Round your answers
to two decimal places (eg. 98.76).
Does there seem to be a possible difference in the two machines?
Plot the first 36 observations in the table on a normal probability plot and the remaining
observations on another normal probability plot. Compare the results with the single normal
probability plot constructed for all of the data.
A separate normal distribution for each group of caps fits the data ____ the distribution for all of
the data. This is to be expected when the mean and standard deviations of the groups ____ as
they do here.
SOLUTION
The sample mean is 21.265 and the sample standard deviation is 6.422.
The first 36 observations:
Sample mean
x
=
18.67
Sample standard deviation
=
4.39
First quartile
Median (second quartile)
Third quartile
The last 32 observations:
Sample mean
x
=
24.19
First quartile
Median (second quartile)
Third quartile