Question
In: Statistics and Probability
Use the following contingency table to complete. A B C Total 1 10 25 55 90...
Use the following contingency table to complete.
| A | B | C | Total | |
| 1 | 10 | 25 | 55 | 90 |
| 2 | 40 | 50 | 60 | 150 |
| Total | 50 | 75 | 115 | 240 |
a. Compute the expected frequencies for each cell.
b. Set up the null and alternative hypotheses to test.
c. Compute X2STAT Is it significant at α=0.01?
d. Compute P-Value
e.Is X2STAT significant at α=0.01?
Solutions
Expert Solution
(a) The second table contains the expected values.
| Chi-Square Independence test - Results |
|
(b) Null and Alternative
Hypotheses The following null and alternative hypotheses need to be tested: H0: The two variables are independent Ha: The two variables are dependent This corresponds to a Chi-Square test of independence. Degrees of Freedom The number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2 Critical value and Rejection Region Based on the information provided, the significance level is α=0.01, the number of degrees of freedom is df = (2 - 1) * (3 - 1) = 2, so the critical value is 9.2103. Then the rejection region for this test becomes R={χ2:χ2>9.2103}. (c)Test Statistics The Chi-Squared statistic is computed as follows: 
(d)P-value The corresponding p-value for the test is p=Pr(χ2>12.3208)=0.0021 (e)The decision about the null hypothesis Since it is observed that χ2=12.3208>χ2_crit=9.2103, it is then concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.01 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive. |
orchestra answered 2 years agoRelated Solutions
Use the following contingency table to complete (a) and (b) below. A B C Total 1...
Use the following contingency table to complete (a) and (b)
below.
A B C Total
1 15 35 40 90
2 30 35 45 110
Total 45 70 85 200
(a). Compute the expected frequencies for each cell.
(b) Compute χ2STAT. Is it significant at α=0.01?
Use the following contingency table to complete (a) and (b) below. A B C Total 1...
Use the following contingency table to complete (a) and (b)
below.
A
B
C
Total
1
15
30
45
90
2
45
50
55
150
Total
60
80
100
240
a. Compute the expected frequencies for each cell.
A
B
C
1
2
(Type integers or decimals.)
b. Compute χ2STAT. is it significant at α=0.005?
Set up the null and alternative hypotheses to test. Choose the
correct answer below.
H0: πA= πB= πC
H1:Not all πj are equal (where j=A,...
use the following contingency table a b c total 1 15 30 45 90 2 40...
use the following contingency table
a
b
c
total
1
15
30
45
90
2
40
45
50
135
total
55
75
95
225
a. compute the expected frequency for each cell
b. compute x^2stat. is it significant at a=0.01
1. Use Table A to Complete Table B. Table A On Taxable Income The Tax Rate...
1. Use Table A to Complete Table B.
Table A
On Taxable Income
The Tax Rate Is
Up to $27,050
20.0%
From $27,051 to $65,550
27.5%
From $65,551 to $136,750
30.5%
From $136,751 to $297,350
35.5%
Over $297,350
39.1%
Table B
Taxpayer
Income
Tax Amount
Average Tax Rate
Mariginal Tax Rate
Giannis
$52,700
Sue
$132,500
Damian
$237,000
Breanna
$315,250
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1. Show that the following wff is a contingency. (A → B) ∧ (B → ¬A)...
1. Show that the following wff is a contingency. (A → B) ∧ (B →
¬A) → A.
2. Show that the following wff is a tautology. (A → (B → C)) →
((A → B) → (A → C)).
3. Determine if the following wff is a tautology, contradiction,
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Complete the following table. (All solutions are at 25 ∘C.) [H3O+] [OH−] pH Acidic or Basic...
Complete
the following table. (All solutions are at 25 ∘C.)
[H3O+]
[OH−]
pH
Acidic or Basic
3.5×10−3
_____
_____
_____
_____
3.8×10−7
_____
_____
1.8×10−9
_____
_____
_____
_____
_____
7.15
_____
Part A
Complete the first column.
Express your answers using two significant figures. Enter your
answers numerically separated by commas.
[H3O+]2, [H3O+]4 =
nothing
M
SubmitRequest Answer
Part B
Complete the second column.
Express your answers using two significant figures. Enter your
answers numerically separated by commas.
[OH−]1,...
The following table shows the total costs for each of four firms (A, B, C, and...
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Firm Unit to be eliminated A B C D
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Three...
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31. Use Table A to complete Table B. TABLE A On Taxable Income The Tax Rate...
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The Tax Rate Is Up to $27,050 20.0% From $27,051 to $65,550 27.5%
From $65,551 to $136,750 30.5% From $136,751 to $297,350 35.5% Over
$297,350 39.1% TABLE B Taxpayer Income Tax Amount Average Tax Rate
Giannis $52,700 Sue $132,500 Damian $237,000 Breanna $315,250
Marginal Tax Rate
You will create a datafile with the following information: 70 80 90 55 25 62 45...
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