1. A small town in Western Massachusetts consists of approximately 5,000 adults,
ID: 3149424 • Letter: 1
Question
1. A small town in Western Massachusetts consists of approximately 5,000 adults, 2,000 who live in private homes while the remaining live in apartment buildings. Of those living in private homes, 240 are upper income, 1,200 are middle income and 560 are lower income. Of those living in apartment buildings, 900 are upper income, 600 are middle income, and 1,500 are lower income. Set up a cross-classification table for type of dwelling unit and income status, to find the probability that a person chosen at random: a. Is type of dwelling unit statistically independent of income?
Explanation / Answer
A small town in Western Massachusetts consists of approximately 5,000 adults, 2,000 who live in private homes while the remaining live in apartment buildings. Of those living in private homes, 240 are upper income, 1,200 are middle income and 560 are lower income. Of those living in apartment buildings, 900 are upper income, 600 are middle income, and 1,500 are lower income. Set up a cross-classification table for type of dwelling unit and income status, to find the probability that a person chosen at random: a. Is type of dwelling unit statistically independent of income?
Private
Apartment
Upper income
240
900
1140
Middle income
1200
600
1800
Lower income
560
1500
2060
Total
2000
3000
5000
Null hypothesis: dwelling unit is independent of income
Null hypothesis: dwelling unit is not independent of income
Chi-Square Test
Observed Frequencies
Column variable
Calculations
private
apartment
Total
fo-fe
upper income
240
900
1140
-216
216
middle income
1200
600
1800
480
-480
lower income
560
1500
2060
-264
264
Total
2000
3000
5000
Expected Frequencies
Column variable
0
private
apartment
Total
(fo-fe)^2/fe
upper income
456
684
1140
102.3158
68.2105
middle income
720
1080
1800
320.0000
213.3333
lower income
824
1236
2060
84.5825
56.3883
Total
2000
3000
5000
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
844.831
Critical Chi square value at 0.05 level =5.991
Calculated chi square =844.831 > 5.991 the table value.
The null hypothesis is rejected.
At the 5% level of significance, dwelling unit is not independent of income.
Private
Apartment
Upper income
240
900
1140
Middle income
1200
600
1800
Lower income
560
1500
2060
Total
2000
3000
5000
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