Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates (Perez, Chung, Stevens) they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? The data from the surveys is recorded in the contingency table below. Perez Chung Stevens Row Total Before 67 28 35 130 After 64 147 75 286 Column Total 131 175 110 416 Which of the following shows the correct first three steps to performing a chi-square Homogeneity Test at the 5% significance level? Select the correct answer below: H0: The distributions of the two populations are the same. Ha: The distributions of the two populations are NOT the same. α=0.05 The test statistic, χ20, is: χ20=(67−40.94)40.94+(28−54.69)54.69+(35−34.38)34.38 +(64−90.06)90.06+(147−120.31)120.31+(75−75.63)75.63=0.09 H0: The distributions of the two populations are NOT the same. Ha: The distributions of the two populations are the same. α=0.05 The test statistic, χ20, is: χ20=(40.94−67)267+(54.69−28)228+(34.38−35)235 +(90.06−64)264+(120.31−147)2147+(75.63−75)275=51.05 H0: The distributions of the two populations are the same. Ha: The distributions of the two populations are NOT the same. α=0.05 The test statistic, χ20, is: χ20=(67−40.94)240.94+(28−54.69)254.69+(35−34.38)234.38 +(64−90.06)290.06+(147−120.31)2120.31+(75−75.63)275.63=43.09 H0: The distributions of the two populations are NOT the same. Ha: The distributions of the two populations are the same. α=0.05 The test statistic, χ20, is: χ20=(67−40.94)240.94+(28−54.69)254.69+(35−34.38)234.38 +(64−90.06)290.06+(147−120.31)2120.31+(75−75.63)275.63=43.09
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates (Perez, Chung, Stevens) they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? The data from the surveys is recorded in the contingency table below. Perez Chung Stevens Row Total Before 67 28 35 130 After 64 147 75 286 Column Total 131 175 110 416 Which of the following shows the correct first three steps to performing a chi-square Homogeneity Test at the 5% significance level? Select the correct answer below: H0: The distributions of the two populations are the same. Ha: The distributions of the two populations are NOT the same. α=0.05 The test statistic, χ20, is: χ20=(67−40.94)40.94+(28−54.69)54.69+(35−34.38)34.38 +(64−90.06)90.06+(147−120.31)120.31+(75−75.63)75.63=0.09 H0: The distributions of the two populations are NOT the same. Ha: The distributions of the two populations are the same. α=0.05 The test statistic, χ20, is: χ20=(40.94−67)267+(54.69−28)228+(34.38−35)235 +(90.06−64)264+(120.31−147)2147+(75.63−75)275=51.05 H0: The distributions of the two populations are the same. Ha: The distributions of the two populations are NOT the same. α=0.05 The test statistic, χ20, is: χ20=(67−40.94)240.94+(28−54.69)254.69+(35−34.38)234.38 +(64−90.06)290.06+(147−120.31)2120.31+(75−75.63)275.63=43.09 H0: The distributions of the two populations are NOT the same. Ha: The distributions of the two populations are the same. α=0.05 The test statistic, χ20, is: χ20=(67−40.94)240.94+(28−54.69)254.69+(35−34.38)234.38 +(64−90.06)290.06+(147−120.31)2120.31+(75−75.63)275.63=43.09
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates (Perez, Chung, Stevens) they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? The data from the surveys is recorded in the
|
|
Perez |
Chung |
Stevens |
Row Total |
|
Before |
67 |
28 |
35 |
130 |
|
After |
64 |
147 |
75 |
286 |
|
Column Total |
131 |
175 |
110 |
416 |
Which of the following shows the correct first three steps to performing a chi-square Homogeneity Test at the 5% significance level?
Select the correct answer below:
H0: The distributions of the two populations are the same.
Ha: The distributions of the two populations are NOT the same.
α=0.05
The test statistic, χ20, is:
χ20=(67−40.94)40.94+(28−54.69)54.69+(35−34.38)34.38 +(64−90.06)90.06+(147−120.31)120.31+(75−75.63)75.63=0.09
H0: The distributions of the two populations are NOT the same.
Ha: The distributions of the two populations are the same.
α=0.05
The test statistic, χ20, is:
χ20=(40.94−67)267+(54.69−28)228+(34.38−35)235 +(90.06−64)264+(120.31−147)2147+(75.63−75)275=51.05
H0: The distributions of the two populations are the same.
Ha: The distributions of the two populations are NOT the same.
α=0.05
The test statistic, χ20, is:
χ20=(67−40.94)240.94+(28−54.69)254.69+(35−34.38)234.38 +(64−90.06)290.06+(147−120.31)2120.31+(75−75.63)275.63=43.09
H0: The distributions of the two populations are NOT the same.
Ha: The distributions of the two populations are the same.
α=0.05
The test statistic, χ20, is:
χ20=(67−40.94)240.94+(28−54.69)254.69+(35−34.38)234.38 +(64−90.06)290.06+(147−120.31)2120.31+(75−75.63)275.63=43.09
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Transcribed Image Text:Continuing the chi-square homogeneity test, a critical value is found and conclusions are made about the null hypothesis.
Perez
67
Chung
28
Row Tatal
Stevens
35
Before
130
40.94
54.69
34.38
64
147
75
After
286
90.06
131
120.31
175
75.63
110
Celuma Tetal
416
• Ho: The distributions of the two populations are the same.
Ha: The distributions of the two populations are NOT the same.
. α- 0.05.
• The test statistic, xỉ = 43.09.
Use this portion of the X2-Table to find the critical value:
...
...
...
...
...
2
4.605
5.991
7,378
9.210
10.597
3
6.251
7.815
9.348
11.345
12.838
4.
7.779 9.488 11.143
13.277
14.860
Which is the correct conclusion of the homogeneity test, at the 5% significance level?
Select the correct answer below:
Degrees of freedom = (r – 1)(c – 1) = 2
Critical value: X10 = 4.605
Conclusion: The test statistic is greater than the critical value (X > Xố10). So, we should reject Ho because the
test statistic falls into the rejection region.
Interpretation: At the 10% significance level, the data provides sufficient evidence to conclude that there has been
a change in political candidate support since the earthquake, because the distributions are NOT the same.
Degrees of freedom = (r – 1)(c – 1) = 2
Critical value: X5 = 5.991
Conclusion: The test statistic is greater than the critical value (X > xỉns). So, we should reject H, because the
o.05
test statistic falls into the rejection region.
Interpretation: At the 5% significance level, the data provides sufficient evidence to conclude that there has been a
change in political candidate support since the earthquake, because the distributions are NOT the same.
Degrees of freedom = (r - 1)(c – 1) = 2
Critical value: X05 = 5.991
Conclusion: The test statistic is greater than the critical value (X > xảns). So, we should NOT reject Ho because
the test statistic falls into the rejection region.
Interpretation: At the 5% significance level, the data does not provides sufficient evidence to conclude that there
has been a change in political candidate support since the earthquake.
Degrees of freedom = (r - 1)(c – 1) = 3
Critical value: X05 = 11.345
Conclusion: The test statistic is greater than the critical value (X > xảns). So, we should reject Ho because the
test statistic falls into the rejection region.
Interpretation: At the 5% significance level, the data provides sufficient evidence to conclude that there has been a
change in political candidate support since the earthquake, because the distributions are NOT the same.
Degrees of freedom = (r – 1)(c – 1) = 3
Critical value: X05 = 11.345
Conclusion: The test statistic is greater than the critical value (Xx > Xố05). So, we should NOT reject Ho because
0.05
the test statistic falls into the rejection region.
Interpretation: At the 5% significance level, the data does not provides sufficient evidence to conclude that there
has been a change in political candidate support since the earthquake.
Solution
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