In an experiment on human behaviour, a sociologist asks four men and four women
ID: 3176016 • Letter: I
Question
In an experiment on human behaviour, a sociologist asks four men and four women to enter a room and sit wherever they wish at a rectangular table. There are three chairs at each side of the table and one at each end. The two end seats are considered to be special in that people sitting there have more dominant positions at the table. The seating experiment is repeated 28 times using new subjects each time. The following table shows the number of times that the two end seats were occupied by two men. by two women and by a man and a woman. Using a Likelihood ratio test, test the hypothesis that the probabilities for the three classes are: 3/14, 3/14 and 8/14.Explanation / Answer
Solution:
We have to test whether the probabilities for the given three classes are 3/14, 3/14 and 8/14 or not. For checking this hypothesis we have to use the asymptotic Chi square distribution. The test statistic formula is given as below:
Chi square = [(O - E)2/E]
Where, O = observed frequency and E = expected frequency
E = total*expected probability
Degrees of freedom = 3 – 1 = 2
We are given
Total = 28
E for MM = 28*0.214285714 = 6
E for FF = 28*0.214285714 = 6
E for MF or FM = 28*0.571428571 = 16
Pair
O
Exp. Prob.
E
(O - E)
(O - E)^2
(O - E)^2 / E
MM
10
3/14 = 0.214285714
6
4
16
2.666666667
FF
4
3/14 = 0.214285714
6
-2
4
0.666666667
MF or FM
14
8/14 = 0.571428571
16
-2
4
0.25
Total
28
1
28
3.583333333
Chi square = [(O - E)2/E] = 3.583333333
P-value = 0.166682134
P-value is greater than alpha value = 0.05, so we do not reject the null hypothesis that the given distribution of frequencies does not follows a specific distribution of frequencies.
We conclude that there is no sufficient evidence that the probabilities for the three classes are 3/14, 3/14 and 8/14.
Pair
O
Exp. Prob.
E
(O - E)
(O - E)^2
(O - E)^2 / E
MM
10
3/14 = 0.214285714
6
4
16
2.666666667
FF
4
3/14 = 0.214285714
6
-2
4
0.666666667
MF or FM
14
8/14 = 0.571428571
16
-2
4
0.25
Total
28
1
28
3.583333333
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.