A? government\'s economic analysis branch recently released figures that they cl
ID: 3129223 • Letter: A
Question
A? government's economic analysis branch recently released figures that they claimed showed a growth spurt in the western region of a certain country that is divided into 5151 states. Using the accompanying? table, where the cell values are numbers of? states, determine if the percent change in real GDP by state was independent of region of the country.
1. What are the null and alternative? hypotheses?
A.
Upper H 0H0?:
GDP? % change is independent of region.
Upper H Subscript Upper AHA?:
GDP? % change increases from east to west.
B.
Upper H 0H0?:
GDP? % change is independent of region.
Upper H Subscript Upper AHA?:
GDP? % change is not independent of region.Your answer is correct.
C.
Upper H 0H0?:
GDP? % change is independent of region.
Upper H Subscript Upper AHA?:
GDP? % change increases from west to east.
D.
Upper H 0H0?:
GDP? % change is not independent of region.
Upper H Subscript Upper AHA?:
GDP? % change is independent of region.
2.
What is the test? statistic?
chi squared ?2 equals= ____
?(Round to two decimal places as? needed.)
3.
What is the? P-value?
?P-value equals=_____
?(Round to three decimal places as? needed.)
4.
What is the proper? conclusion?
A. Fail to reject HO
B. Reject HO
There: (is or is not) sufficient evidence to conclude that GDP? % change (increases from west to east or increases from east to west or is not independent of region or
is independent of region).
GDP % Change Table GDP % Change Bottom 60% Total Top 40% 10 4 Region West Midwest Southeast Northeast Total 15 12 12 12 51 2 21 10 30 Print DoneExplanation / Answer
A government's economic analysis branch recently released figures that they claimed showed a growth spurt in the western region of a certain country that is divided into 5151 states. Using the accompanying table, where the cell values are numbers of states, determine if the percent change in real GDP by state was independent of region of the country.
1. What are the null and alternative hypotheses?
A.Upper H 0H0:GDP % change is independent of region.
Upper H Subscript Upper AHA:GDP % change increases from east to west.
B.Upper H 0H0:GDP % change is independent of region.
Upper H Subscript Upper AHA:GDP % change is not independent of region. Your answer is correct.
C.Upper H 0H0:GDP % change is independent of region.
Upper H Subscript Upper AHA:GDP % change increases from west to east.
D.Upper H 0H0:GDP % change is not independent of region.
Upper H Subscript Upper AHA:GDP % change is independent of region.
2.
What is the test statistic?
chi squared 2 equals= 7.31
(Round to two decimal places as needed.)
3.
What is the P-value?
P-value equals=0.063
(Round to three decimal places as needed.)
4.
What is the proper conclusion?
A. Fail to reject HO ( at 5% level)
B. Reject HO
There: not sufficient evidence to conclude that GDP % change (increases from west to east or increases from east to west or is not independent of region or is independent of region).
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Top40%
Bottom60%
Total
fo-fe
West
10
5
15
3.8235
-3.8235
Midwest
4
8
12
-0.9412
0.9412
Southeast
5
7
12
0.0588
-0.0588
Northeast
2
10
12
-2.9412
2.9412
Total
21
30
51
Expected Frequencies
Column variable
Top40%
Bottom60%
Total
(fo-fe)^2/fe
West
6.1765
8.8235
15
2.3669
1.6569
Midwest
4.9412
7.0588
12
0.1793
0.1255
Southeast
4.9412
7.0588
12
0.0007
0.0005
Northeast
4.9412
7.0588
12
1.7507
1.2255
Total
21
30
51
Data
Level of Significance
0.05
Number of Rows
4
Number of Columns
2
Degrees of Freedom
3
Results
Critical Value
7.8147
Chi-Square Test Statistic
7.3060
p-Value
0.0628
Do not reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Top40%
Bottom60%
Total
fo-fe
West
10
5
15
3.8235
-3.8235
Midwest
4
8
12
-0.9412
0.9412
Southeast
5
7
12
0.0588
-0.0588
Northeast
2
10
12
-2.9412
2.9412
Total
21
30
51
Expected Frequencies
Column variable
Top40%
Bottom60%
Total
(fo-fe)^2/fe
West
6.1765
8.8235
15
2.3669
1.6569
Midwest
4.9412
7.0588
12
0.1793
0.1255
Southeast
4.9412
7.0588
12
0.0007
0.0005
Northeast
4.9412
7.0588
12
1.7507
1.2255
Total
21
30
51
Data
Level of Significance
0.05
Number of Rows
4
Number of Columns
2
Degrees of Freedom
3
Results
Critical Value
7.8147
Chi-Square Test Statistic
7.3060
p-Value
0.0628
Do not reject the null hypothesis