Download MT122Midterm

MT122
Midterm
Summer 2011
Ins.: G. Nazi
Name:____________
(1/2 pt.)
1) The following data represents the number of days absent from school in one school year for a
sample of 40 students in Ms. Jinn’s fourth grade class.
17
6
16
17
a)
8
8
9
8
12
11
3
15
3
0
2
12
0
1
5
5
5
4
15
14
13
19
12
0
Construct a frequency distribution using 7 classes.
Use 0 as your starting point.
Class limits
Tally
b) Construct a frequency Polygon. Label all axes.
12
21
14
12
(3 pts.)
Frequency
(1 pts.)
25
22
20
3
10
9
12
5
2) The data below represents the weights (in pounds) of 40 packages delivered by the postal service.
2
10
19
25
4
10
19
25
4
12
20
25
4
12
20
28
5
12
21
28
5
13
21
28
6
15
21
29
7
15
22
29
8
16
22
30
8
18
23
30
a) What is the variable?
(1/2 pt.)
b) What is the population?
(1/2 pt.)
c)
(1/2 pt.)
What is the sample size used? Is it a large, or a small sample?
d) Find the median.
(1/2 pt.)
e)
Find the mode.
(1/2 pt.)
f)
Find the midrange.
(1/2 pt.)
g) Is the variable discrete or continuous? Explain.
(1/2 pt.)
h) Is the variable nominal, ordinal, interval, or ratio?
(1/2 pt.)
i)
Find P64 .
(1/2 pt.)
j)
Find the percentile corresponding to x  28 .
(1/2 pt.)
3) Decide the best measurement of central tendency for each data set. Justify your answer.
Note: Do not compute the measurements of central tendency; just decide which the best measure
in each case is.
(1 pt. each)
a)
Letter grades:
A, B, B, A, C, C, C, D, F, B.
Best measurement is (circle one): mean
Explain why:
$46,000
$55,000
$485,000
$53,000
$58,000
$61,050
Best measurement is (circle one): mean
Explain why:
midrange
$49,483
$56, 000
$48,000
median
mode
midrange
___________________________________________
___________________________________________
Test Scores: Highest Score = 92, Lowest Score = 55.
Best measurement is (circle one): mean
Explain why:
4)
mode
___________________________________________
___________________________________________
b) Salaries:
c)
median
median
mode
midrange
___________________________________________
___________________________________________
IQ scores for a sample of 8 college students are shown below:
102
100
115
99
104
122
124
120
Find:
a)
Mean
(1 pt.)
b) Standard deviation
x
(2 pt.)
x2
102
100
115
99
104
122
124
120
c)
If the variable IQ scores are normally distributed, then according to the empirical rule,
find the range in which approximately 95% of the scores will fall?
(1 pt.)
5)
A district wishes to study the relationship between class size (x), and achievement test scores (y).
A sample of 8 classrooms from the school district is given in the table below. .
Class Size, x
15
17
18
20
21
24
26
29
a)
Score, y
85
86
84
82
80
78
75
71
Construct a scatter plot for the data. Label all your axes.
b) Calculate the correlation coefficient r , and r 2 .
(1 pt.)
(3 pts.)
c)
Interpret the value of r 2 in context of this problem.
(1 pt.)
d) Find the equation of the regression line for the data.
(3 pts.)
e)
(1 pt.)
Predict the achievement score for a class size of 22.
6) Teachers salaries are normally distributed with mean of $45,000, and standard deviation of
$12,000. Solve using the empirical rule.
a)
What percent of teachers make above $69,000?
b) What percent of teachers make between $21,000 and $57,000?
(1 pt.)
(1 pt.)
7) A study indicates that 4% of American teenagers have tattoos. You randomly sample 30 teenagers.
(1 pt. each)
a)
What is the probability that exactly 3 teenagers will have a tattoo?
b) What is the probability that none will have a tattoo
8)
The mean cholesterol level in children is 175 mg/dL with standard deviation 35 mg/dL. Assume
this level varies from child to child according to an approximate normal distribution. (1 pt. each)
a.
What percentage of children has a cholesterol level above 200 mg/dL?
b.
Find the probability of selecting a child whose cholesterol level is between 165 mg/dL
and 185 mg/dL.
c.
In a sample of 200 children, how many will have a cholesterol level above 170 mg/dL?
d.
How high are the levels for the highest 2% of all children?
9) You pay $10 to play a game of chance. There are thirteen balls in a bag. Five of them are red, three of
them are green, and the rest are yellow. You are to draw one ball from the bag. You will win $14 if
you draw a red ball and you will win $12 if you draw a yellow ball. How much do you expect to win or
lose? Is it a fair game? Explain. (4 pts.)
10) Multiple choice.. Write the letter corresponding to the correct answer on the line provided. (1/2 pt. each).
1)
a)
b)
c)
d)
The science of statistics includes which of the following:
Organizing data.
Presenting data.
Interpreting data.
All of the above.
______
2)
a)
b)
c)
d)
In descriptive statistics our main objective is to:
Describe the population.
Describe the data we collected.
Infer something about the population.
Compute an average.
______
3)
a)
b)
c)
d)
Which of the following statements is true regarding a sample?
It is a part of population.
It must contain at least five observations.
It must be normally distributed.
All of the above.
______
4)
a)
b)
c)
d)
A qualitative variable:
Always refers to a sample.
Is not numeric.
Have only two possible outcomes.
All of the above.
______
5)
a)
b)
c)
d)
A discrete variable is:
An example of a qualitative variable.
Can assume any number values.
Must appear in the form of a count.
Must appear in the form of a measurement.
______
6)
a)
b)
c)
d)
The ordinal scale of measurement:
Has a meaningful zero point.
Is based on ranks.
Is a quantitative variable.
All of the above.
______
7) A study is conducted to find out the percent of High School seniors attend a four year
college. The population is:
______
a) All four year colleges.
b) All High School seniors.
c) The percent of High School seniors.
d) All High School seniors attending a four year college.
8)
a)
b)
c)
d)
Salaries is an example of
Discrete data.
Continuous data.
Nominal data.
Interval data.
______
9)
a)
b)
c)
d)
Religious Affiliations is an example of
Nominal data
Ordinal data
Interval data
Ratio data
______
Use the table below for questions 10 and 11.
Class Limits
1–8
9 – 16
17 – 24
25 – 32
33 – ?
10) The class width is
a) 7
b) 8
c) 9
Frequency
4
8
9
10
1
______
d) 8.5
11) The upper class limits of the last class is
a) 34
b) 38
c) 39
d) 40
______
12) Ranking of college professors (Full professor, Associate professor, assistant professor, …
etc.) is an example of:
______
a) Nominal data
b) Ordinal data
c) Interval data
d) Ratio data
13) The _________ is a number that divides a ranked data set into two equal halves.
______
a) Mean
b) Mode
c) Median
d) Midrange
14)
a)
b)
c)
d)
The standard deviation of 2,2,2,2, and 2 is :
0
1
2
4
______
15)
a)
b)
c)
d)
Zip codes are:
Ordinal data
Discrete data
Quantitative data
None of the above
______
16) In a data set the Highest = 100, and Lowest = 51. If a frequency distribution using 8 classes is
constructed then the class width must be:
______
a) 6
b) 6.5
c) 7
d) 7.5
17) A random sample of 500 households in Vancouver was selected and several variables are
recorded for each household. Which of the following is NOT CORRECT?
______
a) Household total income is a ratio scaled variable.
b) Household total income is a discrete variable.
c) Socioeconomic status was coded as 1=low income, 2=middle income,
3=high income and is an interval scaled variable.
d) The primary language used at home is a nominal scaled variable.
18) The distribution of the heights of students in a large class is bell shaped. Moreover, the
average height is 68 inches, and the standard deviation is 3. Approximately what percent of
the heights is more than 74 inches?
______
a) 2.5%
b) 16%
c) 50%
d) 95%
19) The heights in centimeters of 5 students are: 165, 175, 176, 159, and 170.
The sample median and sample mean are respectively:
a) 170, 169
b) 170, 170
c) 169, 170
d) 176, 169
20)
a)
b)
c)
d)
In general, which of the following statements is FALSE?
The sample mean is more sensitive to extreme values than the median.
The sample standard deviation is a measure of spread around the sample mean.
The sample standard deviation is a measure of central tendency around the median.
None of the above.
______
______
21) The term test scores of 15 students enrolled in a Business Statistics class were recorded in
ascending order as follows: 4, 7, 7, 9, 10, 11, 13, 15, 15, 15, 17, 17, 19, 19, and 20
After calculating the mean, median, and mode, an error is discovered: one of the 15’s is
really a 17. The measures of central tendency which will change are:
______
a) The mean only
b) The mode only
c) The median only
d) The mean and mode
22) If the correlation between body weight (y) and annual income (x) were high and positive, we
could conclude that:
______
a) High incomes cause people to eat less food.
b) Low incomes cause people to eat more food.
c) High incomes cause people to eat more food.
d) High income people tend to be less heavy than low income people, on average.
23) Men tend to marry women who are slightly younger than themselves. Suppose that every
man (x) married a woman (y) who was exactly 0.5 of a year younger than themselves. Which
of the following is CORRECT?
______
a) The correlation is −0.5.
b) The correlation is 0.5.
c) The correlation is 1.
d) The correlation is 0
24) Which is the strongest relationship?
a) r = -0.582
b) r = 0.582
c) r = -0.822
______
d) r = 0
25) In a statistics course, a linear regression equation was computed to predict the final exam
score based on the score on the first test of the term. The equation was, y  25  0.7 x ,
where y is the final exam score and x is the score on the first test. George scored 80 on his
first test, what is his predicted final exam score?
______
a) 80
b) 81
c) 82
d) 91