Aragon Equipment, Inc. is a tractor manufacturer that is beginning to realize the importance of sales data in marketing
Posted: Wed May 04, 2022 12:42 pm
Aragon Equipment, Inc. is a tractor manufacturer that is
beginning to realize the importance of sales data in marketing its
products. Its two main products are The Incisor, a tractor used in
large agricultural settings, and The Caddy, a smaller tractor
primarily used in landscape. The company divides its market into
four geographic regions. With the aim of maximally allocating its
resources, Aragon decides to investigate whether there is a
relationship between the variables type of Aragon tractor
sold ("The Incisor" or "The Caddy")
and geographic region of the sale ("Great
Lakes", "Ohio Valley", "Mid-Atlantic", or "Corn Belt").
The contingency table below summarizes sales data from
500
Aragon tractor sales. Each cell of the table contains
three numbers: the first number is the observed cell frequency
(
fO
); the second number is the expected cell frequency (
fE
) under the assumption that there is no relationship
between the type of tractor sold and the geographic region of the
sale; and the third number is the following value.
=−fOfE2fE−Observed cell frequencyExpected cell frequency2Expected cell frequency
The numbers labeled "Total" are totals for observed
frequency.
Part 1
Fill in the missing values in the contingency table. Round your
expected frequencies to two or more decimal places, and round
your
−fOfE2fE
values to three or more decimal places.
Send data to Excel
Geographic region of the sale
Great Lakes
Ohio Valley
Mid-Atlantic
Corn Belt
Total
Type of tractor
The Incisor
177
75
79.97
0.309
67
89
94.66
0.338
408
The Caddy
33
23
18.03
1.370
9
27
21.34
1.501
92
Total
210
98
76
116
500
Part 2
Answer the following to summarize the test of the hypothesis
that there is no relationship between the type of Aragon tractor
sold and the geographic region of the sale. For your test, use
the
0.05
level of significance.
(a)Determine the type of test statistic to use.
Type of test statistic: ▼(Choose one)
(b)Find the value of the test statistic. (Round to two or more
decimal places.)
(c)Find the critical value for a test at the
0.05
level of significance. (Round to two or more decimal
places.)
(d)Can we conclude that there is a relationship between the type
of Aragon tractor sold and the geographic region of the sale? Use
the
0.05
level of significance.
Yes
No
beginning to realize the importance of sales data in marketing its
products. Its two main products are The Incisor, a tractor used in
large agricultural settings, and The Caddy, a smaller tractor
primarily used in landscape. The company divides its market into
four geographic regions. With the aim of maximally allocating its
resources, Aragon decides to investigate whether there is a
relationship between the variables type of Aragon tractor
sold ("The Incisor" or "The Caddy")
and geographic region of the sale ("Great
Lakes", "Ohio Valley", "Mid-Atlantic", or "Corn Belt").
The contingency table below summarizes sales data from
500
Aragon tractor sales. Each cell of the table contains
three numbers: the first number is the observed cell frequency
(
fO
); the second number is the expected cell frequency (
fE
) under the assumption that there is no relationship
between the type of tractor sold and the geographic region of the
sale; and the third number is the following value.
=−fOfE2fE−Observed cell frequencyExpected cell frequency2Expected cell frequency
The numbers labeled "Total" are totals for observed
frequency.
Part 1
Fill in the missing values in the contingency table. Round your
expected frequencies to two or more decimal places, and round
your
−fOfE2fE
values to three or more decimal places.
Send data to Excel
Geographic region of the sale
Great Lakes
Ohio Valley
Mid-Atlantic
Corn Belt
Total
Type of tractor
The Incisor
177
75
79.97
0.309
67
89
94.66
0.338
408
The Caddy
33
23
18.03
1.370
9
27
21.34
1.501
92
Total
210
98
76
116
500
Part 2
Answer the following to summarize the test of the hypothesis
that there is no relationship between the type of Aragon tractor
sold and the geographic region of the sale. For your test, use
the
0.05
level of significance.
(a)Determine the type of test statistic to use.
Type of test statistic: ▼(Choose one)
(b)Find the value of the test statistic. (Round to two or more
decimal places.)
(c)Find the critical value for a test at the
0.05
level of significance. (Round to two or more decimal
places.)
(d)Can we conclude that there is a relationship between the type
of Aragon tractor sold and the geographic region of the sale? Use
the
0.05
level of significance.
Yes
No