COM3710 - Section 1 - Homework 3




riosjosh


Homework 3 (10 points possible, Due 10-18) COMM 3710

Chi-Square Hand-Calculations



1. Professor Bergstrom recently went to Wendover and played craps. He lost all his money! He was sure one of the dice was loaded. Using his communication skills, he convinced the Pit-Boss to check the dice by rolling one die 225 times and recorded each roll. The results are displayed below. Was the die loaded? Use α = .05. (Remember to state H0 , H1 , a decision rule, and a statement of conclusion following your analysis)



1
2
3
4
5
6
30
51
28
33
50
33



H0: F1 = F2 = F3 = F4 = F5 = F6 ; or there is no difference between the number of times any single side of the dice will show up



H1: Not H0 ; or there is a difference between the number of times any single side of the dice will show up, the dice are loaded



Decision Rule: df = N – 1 = 6 – 1 = 5; alpha = .05, 2-tailed test, critical value = 11.07



Reject H0 if computed value for chi-square meets or exceeds 11.07



Side
FO
Fe
1
30
37.5
2
51
37.5
3
28
37.5
4
33
37.5
5
50
37.5
6
33
37.5











2. The Communication Researcher wants to know if Age influences Marital Satisfaction. The table below shows the distribution of Age and Satisfaction for 105 Couples?” Is there evidence for different satisfaction ratings as a function of age? Use α = .05. (Remember to state H0 , H1 , a decision rule, and a statement of conclusion following your analysis)



|| |||||| Marital Satisfaction
||
Age
Low
Medium
High
Young
15
9
10
Middle Age
9
19
10
Older Adult
11
12
10




H0: F1 = F2 = F3 = F4 = F5 = F6 = F7 = F8 = F9 ; Age makes no difference in marital satisfaction



H1: Not H0; Age makes a a difference in marital satisfaction



Decision Rule: df = (G – 1)*(E – 1) = (3-1)*(3-1) = (2)*(2) = 4; alpha = .05,

critical value = 9.49



Reject H0 if computed value for chi-square meets or exceeds 9.49



|| |||||| Marital Satisfaction

Age
Low
Medium
High
Row Totals
Young
15
9
10
34
Middle Age
9
19
10
38
Older Adult
11
12
10
33
Column Totals
35
40
30
105





Fo
Fe
Fo - Fe
(Fo - Fe)2
(Fo - Fe)2 / Fe
Young (low)
15
11.33
3.67
13.47
1.19
Young (medium)
9
12.95
-3.95
15.60
1.20
Young (high)
10
9.71
0.29
0.08
0.01
Middle Age (low)
9
12.67
-3.67
13.47
1.06
Middle Age (medium)
19
14.48
4.52
20.43
1.41
Middle Age (high)
10
10.86
-0.86
0.74
0.07
Older Adult (low)
11
11
0
0.00
0.00
Older Adult (medium)
12
12.57
-0.57
0.32
0.03
Older Adult (high)
10
9.43
0.57
0.32
0.03
Total




5.00



Chi square is 5



Failed to reject H0: Age is not a factor in marital satisfaction