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Date
Jan 9, 2024
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Math2565 w23mid - Midterm for Winter 2023
Introduction to Applied Statistics (York University)
Studocu is not sponsored or endorsed by any college or university
Math2565 w23mid - Midterm for Winter 2023
Introduction to Applied Statistics (York University)
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York University
MATH 2565 3.0 Introduction to Applied Statistics
Midterm Examination – March 9, 2023, 10:00 a.m.–11:20 a.m.
Last Name:
Given Names:
Student Number:
Signature :
DO NOT WRITE IN THIS AREA
Read the following instructions carefully
1. This exam is
closed
book and
closed
notes.
2. You are allowed to bring a calculator, a ruler, and
one 1-sided “aid-sheet” (8.5” by 11”) . You may
NOT borrow a calculator or a “aid-sheet” from
another student.
3. All work must be done in the free space provided
below for each problem or on the back of the
pre-
ceding page
.
4. No other sheets of paper will be accepted or
marked.
5.
Show all work.
Answers without sufficient sup-
porting work will receive
*no credit*
,
even if
the answers are correct
. Round answers to
3
decimal places if not specified.
6. This exam consists of 5 pages in total.
Ran-
dom Digits Table (Table B) and Standard Normal
Probabilities tables are provided separately.
Question
Max Score
Your Score
1
5
2
10
3
8
4
4
5
14
6
8
7
8
TOTAL
57
1
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Problem 1.
(
5pts
) Circle the correct answer: true (T) or false (F).
(1) The 68-95-99.7 Rule can be applied to any data set.
T
F
(2) The three basic principles of statistical design of experiments are control, blinding, and
repetition.
T
F
(3) The square of the correlation,
r
2
, is the fraction of the variation in the values of
y
that is
explained by the least-squares regression of
y
on
x
.
T
F
(4) The least-squares regression line is fit to a set of data. One of the data points has a positive
residual. Then the point must be influential.
T
F
(5) The mean of the least-squares regression residuals is always 0.
T
F
Problem 2.
(
10pts
) Circle the correct answer (please choose only one answer).
1). Here are four lists of 100 numbers. Which one has the largest standard deviation?
A) 50 ‘0’
s
and 50 ‘100’
s
B) 1, 2, 3,
...
, 100
C) 50 ‘45’
s
and 50 ‘55’
s
D) 100 ‘50’
s
2). An opinion poll is to be given to a sample of 90 members of a local gym. The members are
first divided into men and women, and then a simple random sample of 45 men and a separate
simple random sample of 45 women are taken. This is an example of
A) A simple random sample.
B) A stratified sample.
C) A double-blind simple random sample.
D) A randomized comparative experiment.
3). A free cholesterol screening program is set up in the downtown area during the lunch hour.
Individuals can walk in and have their cholesterol measured for free. One hundred seventy-three
people use the service, and their average cholesterol is 217.8. The value 217.8 is an example of
A) a sample proportion.
B) a statistic.
C) a parameter.
D) a stratum.
4). A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck
are red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13
cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). One card
is selected at random and the denomination is recorded. Which of the following is the correct
sample space
S
for the set of possible outcomes?
A)
S
=
{
red, black
}
.
B)
S
=
{
red, red, black, black
}
.
C)
S
=
{
hearts, diamonds, clubs, spades
}
.
D)
S
=
{
red, black, hearts, diamonds, clubs, spades
}
.
5). The weights (in milligrams) of a species of insect are given as follows.
79
,
116
,
118
,
121
,
124
,
128
,
133
,
137
,
142
,
14
.
6
If we omit the outlier 79,
A) both the mean and the standard deviation will be larger.
B) both the mean and the standard deviation will be smaller.
C) the mean will be larger but the standard deviation will be smaller.
D) the mean will be smaller but the standard deviation will be larger.
2
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Please keep three decimals for all computing results.
Problem 3
. (
8pts
) Data were obtained from the A&W web site for the Total Fat in grams
and the Protein content in grams for various items on their menu. Some summary statistics
are provided:
Total Fat
Protein
Mean
35
.
167
32
.
833
Standard Deviation
10
.
591
10
.
362
Correlation
r
= 0
.
983
(a). (
6pts
) Write down the least-squares regression line of Total Fat on Protein.
(b).
(
2pts
) Based on the equation in (a), when Protein increases by 1 gram, Total Fat
will increase by
grams.
The predicted Total Fat with 30-gram Protein is
grams.
Problem 4.
(
4pts
) If you draw an M&M candy at random from a bag of the candies, the
candy you draw will have one of six colors.
The probability of drawing each color depends
on the proportion of each color among all candies made.
Assume the table below gives the
probabilities for the color of a randomly chosen M&M:
Color
Brown
Red
Yellow
Green
Orange
Blue
Probability
0.3
0.3
?
0.1
0.1
0.1
a). (
2pts
) What is the probability of drawing a yellow candy?
b). (
2pts
) What is the probability of not drawing a red candy?
3
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Problem 5
(
14 pts
). Chocolate bars produced by a certain machine are labeled with 8.0oz.
The distribution of the actual weights of these chocolate bars is Normal with a mean of 8.1oz
and a standard deviation of 0.1oz. A chocolate bar is considered underweight if it weighs less
than 8.0oz (Keep three decimals).
(a). (
8pts
) What proportion of chocolate bars weighs between 8.2 and 8.3oz?
(b). (
6pts
) How should the chocolate bar wrappers be labeled so that only 1% of such bars are
underweight?
Problem 6.
(
8pts
) The 95 students in a statistics class are categorized by gender and by the
year in school. The numbers obtained are displayed below:
Year in school
Gender
Freshman
Sophomore
Junior
Senior
Graduate
Total
Male
1
2
9
17
2
31
Female
24
17
13
7
3
64
Total
25
19
22
24
5
95
a). (
2pts
) What proportion of the statistics students in this class are female freshman?
b). (
2pts
) What proportion of the statistics students in this class are sophomores?
c). (
2pts
) What proportion of the statistics students in this class are male?
d). (
2pts
) The data are going to be summarized by computing the conditional distributions of
year in school for male and female students. What would be the entry for male sophomore?
4
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Problem7.
(
8pts)12publicmiddleschoolsagreetoparticipateinanexperimentwith3reading
methods. Use a diagram to outline a completely randomized design for this experiment. Then
do the randomization to assign schools to treatments (Start at line 142 in Table B).
5
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