QSCI 381
Homework 1: Solutions
Due Oct. 2
Mean: 61.81
Hints:
Remember to read the entire question and answer each part as completely as possible.
On graphs remember to include a title and axis labels.
Remember to include units whenever possible.
1.1.9
False. A population is the collection of all outcomes, responses, measurements, or counts that
are of interests. (2pts)
1.1.18
Sample, because only the age of every third person entering the clothing store is recorded. (2pts)
1.1.22
Population: The students who donate at a blood drive (1pt)
Sample: The students who donate that have type O+ blood (1pt)
1.1.30
Population: Collection of the travel plans of all students at a college (1pt)
Sample: Collection of the travel plans of 496 students surveyed (1pt)
1.1.38
Parameter. 52% is a numerical description of the total number of governors. (1pt)
1.2.5
False. More types of calculations can be performed with data at the interval level than with the
data at the nominal level. (2pts)
1.2.9
Quantitative, because the body temperatures are numerical measurements. (2pt)
1.2.21
Qualitative. Nominal. No mathematical computations can be made and data are categorized by
region. (2pts)
1.3.1
In an experiment, a treatment is applied to part of a population and responses are observed. In an
observational study, a research measures characteristics of interest of a part of a population but
does not change existing conditions. (2pts)
1.3.4
Replication is the repetition of an experiment under the same or similar conditions. It is
important because it enhances the validity of the results. (2pts)
1.3.7
False. Using stratified sampling guarantees that members of each group within a population will
be sampled. (2pts)
1.3.13
Perform an experiment because you want to measure the effect of a treatment of the human
digestive system. (2pts)
1.3.18
(a) The experimental units are the 80 people with early signs of arthritis. The treatment is the
experimental sneaker. (2pts) Notes: An experimental unit is the unit to which you apply a
treatment or the subject receiving the treatment. A treatment is the manipulation that an
experimenter makes.
(b) (Many possibilities) A problem with the design is that the sample size is small. The
experiment could be replicated to increase validity. (2pts)
(c) In a placebo-controlled, double-blind experiment neither the subject nor the experimenter
knows whether the subject is receiving a treatment or a placebo. The experimenter is informed
after all the data have been collected. (2pts)
(d) The groups could be randomly split into 20 males and 20 females in each treatment group.
(1pt)
1.3.25
Stratified sampling is used because a sample is taken from each one-acre subplot. Explanations
of potential bias vary. (2pts)
1.3.34
The question is biased because it already suggests that text messaging while driving increases the
risk of a crash. The question might be rewritten as “Does text messaging while driving affect the
risk of a crash?” Notice that the re-written, unbiased question does not use the word increase or
make other suggestions as to the relationship between texting and driving. (2pts)
2.1.7
False. Class width is the difference between the lower or upper limits of consecutive classes.
(2pts)
2.1.12
Class width = 13; lower class limits: 12, 25, 38, 51, 64, 77; Upper class limits: 24, 37, 50, 63, 76,
89 (3pts)
2.1.16
(a) Class width = 10 (1pt)
(b) and (c) (2pts)
Class
0-9
10-19
20-29
30-39
40-49
50-59
60-69
Midpoint
4.5
14.5
24.5
34.5
44.5
54.5
64.5
Class Boundaries
-.5-9.5
9.5-19.5
19.5-29.5
29.5-39.5
39.5-49.5
49.5-59.5
59.5-69.5
2.1.20
(a) Number of classes = 7 (1pt)
(b) Least frequency = 100 (1pt)
(c) Greatest frequency = 900 (1pt)
(d) Class width = 5 (1pt)
2.1.21
(a) 50 (1pt)
(b) 22.5-23.5 pounds (1pt)
2.1.36
relative
cumulative
frequency
class
frequency midpoint frequency
10-24
11
17
0.3438
25-39
9
32
0.2813
40-54
6
47
0.1875
55-69
2
62
0.0625
70-84
4
77
0.125
(2pts for the frequency distribution)
11
20
26
28
32
Rela%ve frequency ATM Withdrawals amount (in dollars) 3pts for the histogram. There must be a title, horizontal axis label with units, and relative
frequency as the vertical axis (the problem asks for relative). The bars should be touching or
close to touching and should represent the data in your frequency distribution.
Class with greatest relative frequency: 10-24 (1pt)
Class with least relative frequency: 55-69 (1pt)
2.1.48
class
976-1103
1104-1231
1232-1359
1360-1487
1488-1615
frequency relative frequency
1
0.02
1
0.02
4
0.08
6
0.12
7
0.14
1616-1743
1744-1871
1872-1999
2000-2127
2128-2255
9
6
8
5
3
0.18
0.12
0.16
0.1
0.06
(a) (3pts). Must have title and axis labels. Bars should be close or touching.
(b) 62%; the sum of the relative frequencies of the class starting with 1616 and all classes with
higher scores is .62 (2 pts)
(c) A score of 1360 or above because the sum of the relative frequencies of the class starting with
1360 and all classes with higher scores is 0.88. (2pts)
2.2.6
D (1pt)
2.2.19 (3 pts total = 1pt for key + 1 for ordered data + 1 general)
Key: 4 │3 = 4.3
4│3 9
5│1 8 8 8 9
6│4 8 9 9 9
7│0 0 2 2 2 5
8│0 1
2.2.29
Temperature (in F) Daily High Temperatures in May Day of the month (3pts)
2.2.35
(a) The graph is misleading because the large gap from 0-90 makes it appear that the sales for the
3rd quarter are disproportionately larger than the other quarters (1 pt)
(b) Redraw the bar graph and begin the y-axis at 0 and increase in even intervals. Include labels
and title (1pt)
2.2.37
(a) The graph is misleading because the angle makes it appear as though the 3rd quarter had a
larger percent of sales than the others, when the 1st and 3rd quarters have the same (1pt)
(b) Redraw pie chart as 2 dimensional. Be sure to include labels and percents (1pt)