Download Math 109 exam I practice

Math 110 Exam I
Past Exam Problems
1) Give an example of a continuous variable.
2) Compute the sample standard deviation for x=5, 6, 8, 10, 11
3) Describe the sampling method used for each of the following:
a) From a list of 1000 ID numbers, choose a starting point by chance and then select every 10th ID
number.
b) 25 students are randomly selected from each grade level at a high school and surveyed about
their study habits.
4) The following data points are the test scores for a statistics class. Compute each of the following:
a)
50
P60
18
b) percentile of 13
c)
Q3
13 80 14 38 11 13 39 41
5) Compute the sample standard deviation: x = 1, 5, 8, 10.
6)
Class
1.3-1.8
1.9-2.4
Frequency
2
12
2.5-3.0
6
a) Construct a relative frequency histogram.
b) Compute the mean.
7)
5, 9, 11, 14, 15, 17, 19, 23
a) Construct a frequency table using 5 as a starting point and class width of 7.
b) Construct a relative frequency histogram. You must first find the class boundaries.
8) Compute a) percentile of 21 b) box plot for the following 12 values:
14 16 21 34 38 39 41 45 50 53 82 90
9) Use the following frequency table to compute the mean:
Class
Frequency
0-4
6
5-9
7
10) (2 points each) The average annual salary of the CSULA professors is $80,000.
a) Identify the population of the study.
b) Is $80,000 a parameter or statistic? Justify your answer.
c) Is $80,000 quantitative or categorical? Justify your answer.
11) Identify the sampling method used:: An social scientist is studying the effect of education on
salary and conducts a survey of 200 selected workers from each of the following categories:
less than a high school degree; high school degree; more than high school degree.
12) A researcher wants to investigate a correlation between meth use as a teen, and having marital
problems as an adult.
a) Identify the population.
b) Which type of study is more appropriate: observational or experimental? Justify your answer
13) For the following 9 values, find a)
Q1
b) percentile of 12
1, 3, 5, 7, 7, 11, 11, 12, 12
14) ( 3 points) Locate the mean, median and mode for the graph shown below:
Median ___
Mode_______ Mean_______
15) Which set has a smaller standard deviation:
A: weights of the NFL linebackers
B: weights of the CSULA students
16) Identify the sampling technique used in the following study: In an effort to determine customer
satisfaction, Delta Airline randomly select 59 flights during certain week and survey some passengers
on those flights.
17) (2 points each) Fill in the blank
a) If the distribution of a random variable is skewed to the right, the value of the mean is ______________
than the value of the median.
b) A ______________sample is the one in which respondents themselves decide whether to be included in
the sample and often reflects opinions of those with strong interests.
c) The running time of a randomly selected movie is an example of ___________________ variable.
d)
A researcher divides the population into three groups by their incomes: low, medium, and high.
Then he selects a random sample from each group. He used __________________________ sampling
method in this study
18)
a) A correlation between two variables does not imply one is a ___________ of the other.
b) In a ________________
study, data are collected from the past by going back in time.
c) In _________________ sampling method, every nth item is selected.
d) A _____________________ is a numerical measurement of a population.
e) To apply the 68-95-99.7 principle, the distribution of the variable must be _________-___________.
f)
When the effects of one factor cannot be separated from the effects of some other factors, the
effects are said to be_______________________.
g) When the researcher controls the assignment of members to different groups, the study is
__________________ study .
h) True/false: If the distribution is skewed, we are usually better off with the mean than the median.
19) (3 points) Choose the data set with a smaller standard deviation. Justify your answer.
A) The IQ scores of all CSULA students.
B) The IQ scores of all CSULA students majoring in mathematics.
20) (3 points) I
A retail store manager wants to conducts a study regarding the shopping habits of his customers. He selects
60 customers who enter his store on a Tuesday morning.
a) Identify the sampling method used in the study.
b) Is the sample representative of the population? Justify \your answer
21) A study finds male children born to women who smoke during pregnancy run a higher risk of criminal
behaviors that last into adulthood than male children born to women who do not smoke.
a) (2 points) Determine whether this study is observational or experimental.
b) (2 points) Can we say smoking during pregnancy is responsible for higher criminal behavior?
Justify your answer
22) 3 points) Identify the sampling method used: A random sample of 100 people from each of five
different age categories was selected.
23) A question is posed on the ESPN website asked visitors to the site to say whether they thought that
marijuana should be legally available for medical purposes.
a) Identify the population.
b) Identify the sample.
c) Is the study cross sectional, prospective, or retrospective? Justify your answer.
d) Is the sample likely to be representative of the population? Justify your answer.
24) The MLB reports that the average annual salary of the major league baseball players is $5,100,000.
a) Identify the population of the study.
b) Is $5.1 M a parameter or statistic? Justify your answer.
25) (2 points) Classify the following variable as quantitative or categorical:
Colors of baseball uniforms ..
26) In a recent study, subjects were randomly assigned to two groups, and one group was given an herb
and the other group a placebo. After 6 months, the numbers of respiratory tract infections each group
had were compared.
a)
Is the study cross sectional, prospective, or retrospective? Justify your answer.
b) Is the study observational or experimental? Justify your answer.
27)
a ) True/false In an observational study, a definite cause-and-effect cannot be shown
a) In an experimental study, the subjects in the _______________ group receive a dummy treatment,
enabling the researchers to control for the placebo effect.
Answers
1)
2)
(Warning: Some answers may not be correct.)
x = height of a man is an example of a continuous variable.
x=5, 6, 8, 10, 11
x
5  6  8  10  11
8
5
X
(x  x)2
5
(5  8) 2  9
6
(6  8) 2  4
8
(8  8) 2  0
10
(10  8) 2  4
11
(11  8) 2  9
  23
Thus the standard deviation is
23
 2.4
4
3) A) systematic b) stratified
4) a)
P60  10(0.6)  6 , a whole number.
Thus
6th  7th 38  39

 38.5
2
2
# of values less than 13 1

 100  10  13  p10
10
10
c)
b) percentile of 13=
Q3  p75  10(0.75)  7.5
Thus take 8th value, which is 41.
5)
x
1  5  8  10
6
4
X
(x  x)2
1
(1  6) 2  25
5
(5  6) 2  1
8
(8  6) 2  4
10
(10  6) 2  16
  46
Thus the standard deviation is
46
 3.9
3
6)
Frequency
Class Bd
Cumulative
Class
Distribution
Midpoint
Freq(mid)
1.3-1.8
2
1.25-1.85
2
1.55
3.1
1.9-2.4
12
1.85-2.45
14
2.15
25.8
2.5-3.0
6
2.45-3.05
20
2.75
16.5
Total
N=20
The mean is 45.4/20=2.27
20
  45.4
, a decimal number.
7) Use class boundaries for the histogram
Frequency
5-11
12-18
19-25
Total
3
3
2
8
Class
Boundaries
4.5-11.5
11.5-18.5
18.5-25.5
Cumulative
Distribution
3
6
8
8
Relative
frequency
37.5%
37.5%
25%
100%
8)
# of values less than 13 2
  100  17  21  p17 b) Need
10
12
3rd  4th 21  34

 27.5 Q2  p50  12(0.5)  6
Q1 , Q2 , Q3 : Q1  p25  12(0.25)  3 ,
2
2
6th  7th 39  41
9th  10th 50  53

 40 . Q3  p75  12(0.75)  9

 51.5
2
2
2
2
a) percentile of 13=
14
27.5
40
51.5
, a whole number:
90
9)
Frequency
0-4
5-9
6
7
  13
Class
midpoint
2
7
(Class mid)(freq)
12
49
  61
The mean is 61//13 = 4.7
10) a) all CSULA professors. B) $23,000 is more likely to be a parameter. The salaries of the CSULA
professors are available to the public. C) quantitative: salaries can be measured numerically.
11) This is stratified: a random sample is taken from each subgroup.
12) A) all married adults B) observational; it is unethical to make people in the control group use meth.
13) ) a)
Q1 : 9(0.25)  2.25  3rd  5
b) There are 7 values less than 12.
7
(100)  78  12  p78
9
14) Medan: A mode: B mean C: The mode is the highest point of the graph. The mean is to the right of the
median (the distribution is skewed to the right)
15) The weights of NFL linebackers have a smaller standard deviation: NFL linebackers all have similar body
type, where as CSULA students have different physique.
16) Cluster : here the subgroups are the flights. Random samples are taken from some of the subgroups, not
all.
17) a) greater b) voluntary c) fixed, independent d) continuous e) stratified f) 64
18) a) cause b) retrospective c)systematic d) parameter e) bell-shaped f) confounded g) experimental h) true
(since the median is not affected by a small number of extreme values)
19) B has a smaller standard deviation. Math majors are all intelligent with high IQs.
Thus the variation of IQ
scores among the math majors would be smaller.
20) )a) Convenience. B) No. Many customers cannot visit the store on Tuesday due to obligations such as
work, school, going to the gym.
21)
a) It is observational. We cannot make people smoke cigarettes.
10) No. In observational studies, effects are often confounded.
For example, smokers tend to
have lower educational attainments and lower SES than nonsomkers and children from low
SES families exhibit higher criminal behavior.
22) This is stratified since SRS is taken from each subgroup.
23) a) all EPSN site visitors b) people who responded to the survey. C) This is a cross sectional
study. d) No. This is a voluntary response sample. People who respond are more likely to have
strong opinions on the topic.
24) a) all major league baseball players. b) it is more likely to be a parameter: the salary data are
stored in a database and the average salary can easily be computed.
25) It is categorical: it can be classified: red, blue, grey, etc but cannot be measured.
26)
a) The study is prospective. The study participants meet with the researchers at least twice. Once when the
study began, then again six month later.
b) It is an experimental study: the researchers randomly assign people into the herb group and the placebo
group
27) a) true b) control
(The following formulas will be provided
2
x  mean 2  ( x  x )
z
s 
, s  s2
std .dev
n 1
,
mean 
 (frequency) (midpoint)
n