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

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 3CST

See similar textbooks

Question

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

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

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

by Bartleby Expert

SEE SOLUTION