Homework 5Students in rural, suburban and urban schools were asked whether good grades, athletic ability, or popularity
was most important to them. A two-way table separating the students by area and by choice of most important
factor is shown below. Using alpha = 0.005, is there a relationship between area and most important goals?
Goals
Grades
Popularity
Sports
Total
Rural
57
50
42
Suburban
87
42
22
Urban
24
6
5
Total
Suburban
Urban
Total
Define Null and Alternative Hypothesis
H0 :
H1 :
State Alpha
Calculate Degrees of Freedom
State Decision Rule
If x2 is greater than β¦
Calculate Test Statistic
Expected values:
Goals
Grades
Popularity
Sports
Total
!
Rural
(πππ πππ£ππ β ππ₯ππππ‘ππ)!
ππ₯ππππ‘ππ
Find x2 =
Results
πππ
!
(π β π)!
π
Homework 5
A public opinion poll surveyed a simple random sample of 100 voters. Respondents were classified by gender
(male or female) and by voting preference (Republican, Democrat, or Independent). Results are shown in the
table below. Using alpha = 0.005, is there a relationship between Gender and Voting Preferences?
Male
Female
Total
Republican
200
250
450
Democrat
150
300
450
Independent
50
50
100
Total
400
600
1000
Independent
50 (40)
50 (60)
100
Total
400
600
1000
Define Null and Alternative Hypothesis
H0 :
H1 :
State Alpha: .005
Calculate Degrees of Freedom 2
State Decision Rule
If x2 is greater than β¦ 10.597
Calculate Test Statistic (use two decimal places)
Expected values:
Male
Female
Total
!
Republican
200 (180)
250 (270)
450
(πππ πππ£ππ β ππ₯ππππ‘ππ)!
ππ₯ππππ‘ππ
Democrat
150 (180)
300 (270)
450
πππ
!
(π β π)!
π
E1,1 = (400 * 450) / 1000 = 180000/1000 = 180
E1,2 = (400 * 450) / 1000 = 180000/1000 = 180
E1,3 = (400 * 100) / 1000 = 40000/1000 = 40
E2,1 = (600 * 450) / 1000 = 270000/1000 = 270
E2,2 = (600 * 450) / 1000 = 270000/1000 = 270
E2,3 = (600 * 100) / 1000 = 60000/1000 = 60
Find x2 = 16.2
Ξ§2 = (200 – 180)2/180 + (150 – 180)2/180 + (50 – 40)2/40 + (250 – 270)2/270 + (300 – 270)2/270 + (50 – 60)2/60
Ξ§2 = 2.22 + 5.00 + 2.50 + 1.48 + 3.33 + 1.67 = 16.2
Results: REJECT THE NULL HYPOTHESIS β GENDER AND VOTING PREFERENCES ARE RELATED
The Chi-Square Distribution
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