University of Southeastern Philippines
eBA 201 Managerial Statistics
Exercise 6.4 – Nonparametric Test
Name: NATHAN KIT A. BERRO
1. Use the following contingency table and the chi-square test of independence to determine
whether social class is independent of the number of children in a family. Let a= 0.05.
Show the steps in testing hypothesis
Number of Social Class
children Lower Middle Upper
0 7 18 6
1 9 38 23
2 or 3 34 97 30
More than 3 47 31 58
Solution:
Step 1: H0: There is no significant relationship between social class and number of children in a
family.
H1: There is a significant relationship between social class and number of children in a
family.
Step 2: The level of significance is set at 0.01.
Step 3: The test statistic is the chi-square distribution.
Step 4: The degrees of freedom equal (r-1)(c-1) or 4. The critical x2 at 4 d.f is 13.21, or if p <
.01, reject the null and accept the alternate.
Step 5: A data table below shows the contingency table;
Observed Frequencies (fo)
Number Grand
Social Class Total
of
children Lower Middle Upper
0 7 18 6 31
1 9 38 23 70
2 or 3 34 97 30 161
More
than 3 47 31 58 136
Grand
Total 97 184 117 398
eBA 201 Managerial Statistics
Exercise 6.4 – Nonparametric Test
Name: NATHAN KIT A. BERRO
1. Use the following contingency table and the chi-square test of independence to determine
whether social class is independent of the number of children in a family. Let a= 0.05.
Show the steps in testing hypothesis
Number of Social Class
children Lower Middle Upper
0 7 18 6
1 9 38 23
2 or 3 34 97 30
More than 3 47 31 58
Solution:
Step 1: H0: There is no significant relationship between social class and number of children in a
family.
H1: There is a significant relationship between social class and number of children in a
family.
Step 2: The level of significance is set at 0.01.
Step 3: The test statistic is the chi-square distribution.
Step 4: The degrees of freedom equal (r-1)(c-1) or 4. The critical x2 at 4 d.f is 13.21, or if p <
.01, reject the null and accept the alternate.
Step 5: A data table below shows the contingency table;
Observed Frequencies (fo)
Number Grand
Social Class Total
of
children Lower Middle Upper
0 7 18 6 31
1 9 38 23 70
2 or 3 34 97 30 161
More
than 3 47 31 58 136
Grand
Total 97 184 117 398
