1. For his Mathematical Studies Project a student gave his classmates a questionnaire to fill out. The results for the question on the gender of the student and specific subjects taken by the student are given in the table below, which is a 2 × 3 contingency table of observed values.
|
|
History |
Biology |
French |
|
|
Female |
22 |
20 |
18 |
(60) |
|
Male |
20 |
11 |
9 |
(40) |
|
|
(42) |
(31) |
(27) |
100 Grande Total |
The following is the table for the expected values.
|
|
History |
Biology |
French |
|
Female |
p= [(42)(60)]/100 |
18.6 [(31)(60)]/100 |
16.2 [(27)(60)]/100 |
|
Male |
q= [(42)(40)]/100
|
r= [(31)(40)]/100
|
10.8 [(27)(40)]/100 |
(a) Calculate the values of p, q and r.
Solution: place the observed matrix into your calculator and then gp tp STAT ->TEST ->CHI-SQUARE TEST (LOOKS LIKE X^2)->ENTER ->CALCULATE.
Now go back to your Matrix and see the expected matrix your calculator created for you.
(3)
The chi-squared test is used to determine if the choice of subject is independent of gender, at the 5% level of significance.
(b) (i) State a suitable null hypothesis H0.
Gender and subject preference are independent.
(ii) Show that the number of degrees of freedom is two.
(r - 1)(c - 1) therefore, (2 - 1)(3 - 1) = 2
(iii) Write down the critical value of chi-squared at the 5% level of significance.
You look up the critical value using the degrees of freedom (2) and the alpha value (.05) which in this case is 5.99
(3)
(c) The calculated value of chi-squared is 1.78. Do you accept H0? Explain your answer.
The rule of thumb is if O.V. is greater than C.V. you reject the null. Since O.v. is 1.78 and the C.V. is 5.99 we FAIL TO reject the null
(2)
(Total 8 marks)
|
|
History |
Biology |
French |
|
|
Female |
22 |
20 |
18 |
(60) |
|
Male |
20 |
11 |
9 |
(40) |
|
|
(42) |
(31) |
(27) |
|
|
|
History |
Biology |
French |
|
Female |
p |
18.6 |
16.2 |
|
Male |
q |
r |
10.8 |
