MTH 133
EXAM 1
1) What is statistics? – Statistics is the science of collecting, organizing,
summarizing and analyzing information in order to draw conclusions.
2) What is the difference between a population and a sample? Provide
examples. – A population is the group to be studied in a statistical analysis and
a sample is a smaller subset of that population, e.g. a population could be all of
the residents of Lenawee county and a sample would be 1000 randomly
selected people from that group.
3) A study was conducted to determine if listening to heavy metal music
affects critical thinking. To test the claim, 114 subjects were randomly
assigned to two groups. Both groups were administered a basic math
skills exam. The first group took the exam while heavy metal music was
piped into the exam room, while the second group took the exam in a silent
room. The mean exam score for the first group was 80, and the mean exam
score for the second group was 87. The researchers concluded that heavy
metal music negatively affects critical thinking. Identify:
a) the research objective – to find out if heavy metal music affects critical
thinking
b) the sample - 114 randomly selected subjects
c) the descriptive statistics – The mean exam score for the group who took the
test while listening to heavy metal music was 80, the mean exam score for the
group who took the test without heavy metal music was 87.
d) the conclusions – Heavy metal music negatively affects critical thinking.
3) Classify the numbers on the shirts of a girl's soccer team as qualitative
data or quantitative data.
A) qualitative data B) quantitative data
4) Classify the number of seats in a movie theater as qualitative data or
quantitative data.
A) qualitative data B) quantitative data
5) The number of violent crimes committed in a day possesses a
distribution with a mean of 1.1 crimes per day and a standard deviation of
four crimes per day. A random sample of 70 days was observed, and the
sample mean number of crimes for the sample was calculated. The data
that was collected in this experiment could be measured with a
__________ random variable.
A) continuous B) discrete
6) Classify the following random variable according to whether it is
discrete or continuous.age of the oldest student in a statistics class
A) discrete B) continuous
7) N/A
8) The following frequency distribution represents the total ticket sales for
5 major rock acts for concerts on March 3, 2005 in various New York City
venues:
Band
# of tickets sold
Metallica
10,735
Slipknot
9,422
Mastodon
1,064
Slayer
3,456
Machine Head
732
a) Construct a relative frequency distribution
Band
# of tickets sold
Relative Frequency
Metallica
10,735
.422
Slipknot
9,422
.371
Mastodon
1,064
.042
Slayer
3,456
.136
Machine Head
732
.029
b) What percentage of tickets were sold by Metallica? 42.2%
c) Construct a frequency bar graph
12000
10000
8000
6000
4000
2000
He
ad
M
ac
hin
e
Sl
ay
er
on
M
as
to
d
no
t
Sl
ip
k
M
et
all
ic
a
0
d) Construct a relative frequency bar graph.
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Metallica
Slipknot
Mastodon
Slayer
Machine
Head
e) Construct a pie chart
3%
14%
4%
42%
Metallica
Slipknot
Mastodon
Slayer
Machine Head
37%
9) Using the data for per capita income for Michigan counties, do the
following:
a) Construct a frequency distribution of the data.
b) Construct a relative frequency distribution of the data (can be put in the
same table as part a)
Income
14000-15999
16000-17999
18000-17999
20000-21999
22000-23999
24000-25999
26000-27999
28000-29999
30000-31999
32000-33999
34000-35999
36000-37999
38000-39999
40000-41999
42000-43999
Frequency
3
15
18
13
14
9
5
3
1
0
1
0
0
0
1
Relative Frequency
0.036
0.18
0.217
0.157
0.169
0.108
0.06
0.036
0.012
0
0.012
0
0
0
0.012
c) Construct a frequency histogram of the data. Describe the shape of the
distribution
20
15
10
5
0
Income
14000-15999
18000-17999
22000-23999
26000-27999
30000-31999
34000-35999
38000-39999
42000-43999
16000-17999
20000-21999
24000-25999
28000-29999
32000-33999
36000-37999
40000-41999
The distribution is skewed right.
10) The following data represent the number of hours a group of 40
community college students studied each day:
1.2
.3
4.5
2.3
3.2
3.2
1.7
1.9
3.4
.1
.9
6.5
3.4
2.4
1.3
1.6
2.8
.7
.1
3.4
3.5
2.7
2.9
2.2
3.1
1.5
1.7
1.9
3.9
3.3
2.9
2.8
1.6
.7
2.8
2.0
3.0
3.1
2.6
2.7
a) Compute the mean – 2.395
b) Compute the range – 6.4
c) Compute the variance – 1.54
d) Compute the standard deviation – 1.24
e) Pick a random sample of 10 students and repeat a through d
1.2
4.5
1.5
2.8
1.7
f) Compute the mean – 2.23
g) Compute the range – 3.6
.9
2.4
1.6
3.5
2.2
h) Compute the variance – 1.24
i) Compute the standard deviation – 1.11
11) A random sample of 30 new cars was taken to find out how many days
a new vehicle can go before it must be professionally repaired (excluding
routine oil changes). The study found a mean of 325 days, with a standard
deviation of 30 days. Assume that a histogram of the data turns out to be
bell shaped.
a) 99.7% of the cars will go between 235 and 415 days before having to be
repaired.
b) Determine the percentage of cars that will go between 265 and 385 days
without needing repair. 95%
c) If the auto company guarantees free repair for cars up until 265 days, what
percentage of cars will they have to repair for free? 2.5%
12) Joe receives the following list of grades at the end of his winter term:
Biology
78
English
87
Mathematics
65
French for Beginners
70
Adventures in Art
95
:
a) Based on this information, what is his grade average for the term? 79%
b) What would Joe have to make in Math to give himself a grade average of 85?
95%
c) Assuming that Biology, English and Math are all worth 3 credits, and French
and Art are 2, what is his grade average? 78.46%
d) Given this situation, what would Joe have to make in Math to yield a grade
average of 85? 93.33%
13) The following data represent the number of live multiple delivery births
(three or more babies for women 15-49 years old:
Age
Number of Multiple Births
15-19
78
20-24
385
25-29
1587
30-34
2854
35-39
1986
40-44
243
45-49
56
a) Approximate the arithmetic mean and the standard deviation age. Mean =
32.03, Standard deviation = 5.04
14) The following data represent the results of a study of 1000 random men
and women between the ages of 15 and 49 to find out how many days a
year they spend thinking about statistics.
Age
Days thinking about Statistics
15-19
2
20-24
24
25-29
56
30-34
125
35-39
245
40-44
98
45-49
21
a) Approximate the arithmetic mean and the standard deviation age. Sample
Mean = 35.45, Standard deviation = 5.63
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