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School
William Rainey Harper College *
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Course
165
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
2
Uploaded by DrDanger12720
MTH165
Quiz 12
Name:_______________________
Section:__________
1.
In the year 2018, the proportions of Dr. C’s Cookie sales across the country were as follows:
Region
Northeast
Midwest
South
West
Proportion
0.190
0.230
0.354
0.226
The data below are from a recent random sample of Dr. C’s Cookie Sales in 2019:
Region
Northeast
Midwest
South
West
Observed Counts
1025
1030
1800
1145
a.
Fill in the following:
Observed Frequency
1025
1030
1800
1145
Expected Frequency
950
1150
1770
1130
b.
Does the distribution of current cookie sales in 2019 differ from the
distribution of Dr. C’s Cookie sales
in the year 2018? Use a 0.05 level of significance.
H:
H
0
: The distribution of cookie sales in 2019 is the same as the distribution of cookie sales in 2018
H
A
: The distribution of cookie sales in 2019 differs from the distribution of cookie sales in 2018
A:
1.
A random sample was taken
2.
The expected frequencies for all categories are at least 5
3.
No N is given so we will assume N is greater than or equal to 100000
N:
The assumptions for the X
2-
GOF Test have been met
T: Just state the value, you do not need to show the computation.
X
2
= 19.15
O:
p-value = .0003
M:
Since the p-value is less than or equal to .05, we reject H
0
S:
There is significant evidence to conclude that the distribution of cookie sales in 2019 differs from the
distribution of cookie sales in 2018
MTH165
Quiz 12
Name:_______________________
Section:__________
2.
In a recent survey of Environmentalists and Non-environmentalists, a random sample of adults was asked,
“How important are moral values when deciding how to vote?”
.
Test if there is an association/dependence
between environmental stance and the importance of moral values on voting using a 0.01 level of significance.
Environmentalist
Non-environmentalist
Morality is Important
740
(
745.4
)
320
(
314.6
)
Morality is Not Important
165
(
159.6
)
62
(
67.4
)
a.
In each set of parentheses above, write the expected value for that cell assuming independence.
Use Matrix B on your calculator to find the expected values.
Round answers to the nearest tenth
.
b.
Run the hypothesis test and state your conclusion.
H:
H
0
: Whether or not morality is important and whether an adult is an Environmentalist or not are independent
H
A
: Whether or not morality is important and whether an adult is an Environmentalist or not are dependent
A:
1.
A random sample was taken
2.
The expected frequency of each cell is at least 5
3.
Since no N is given we will assume N is greater than or equal to 25740
N:
The assumptions for the X
2
independence test have been met
T: Show the formula
without and with
numbers.
X
2
=
∑
all cells (observed
–
expected)
2
/expected
X
2
= ((740
–
745.40)
2
/745.4) + ((320
–
314.6)
2
/314.6) + ((165
–
159.6)
2
/159.6) +((62
–
67.4)
2
/67.4) = .74
O:
p-value = .3894
M:
Since the p-value is greater than .01, we fail to reject H
0
S:
There is not significant evidence to conclude that whether or no morality is important and whether or not an
adult is an Environmentalist are dependent for all adults
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