Question

50 students selected at random from 500 students enrolled in a computer crash

programme were classified according to the age and grade points giving the

following data:

Age (in years)

Grade Point Below 20 21-30 Above 30

Up to 5 - 3 5 2

5.1 to 7.5 - 8 7 5

7.6 to 10.0 - 4 8 8

Test at 5% level of significance that age and grade points are independent

Answer 1

The hypotheses to be tested are;

H₀: age and grade points are independent

H₁: age and grade points are associated.

First , obtain the row and column total observed values (Table 1)

Calculate the expected values using the formula;

$E=\frac{\text{row total * column total}}{\text{total observations}}$

The calculated expected values are on table 2.

Finally calculate the chi-square statistic in table 3 using;

$\chi^2=\sum\frac{ (observed-expected)^2}{expected}$

$\chi ^2=2.875$

The degrees of freedom are V=(c-1)(r-1)=(3-1)(3-1)=4

check the critical value from the chi-square table;

$\chi^2_{0.05(4)}=9.488$

since the test statistic is less than the critical value; fail to reject the null hypothesis.

Age and grade points are independent.