A random sample was taken of 300 undergraduate students from

A random sample was taken of 300 undergraduate students from a university. The students in the sample were classified according to their gender and according to the choice of their major. The result is given in the following table.

Gender Art & Sciences Engineering Business Others Total

Male 75 40 24 66 205

Female 45 12 15 23 95

Total 120 52 39 89 300

Test the hypothesis that the choice of the major by undergraduate students in this university is independent of their gender. Use = 0.01.

Solution

The observed values are

75   40   24   66
45   12   15   23

Setting up an expected values table,

82   35.53333333   26.65   60.81666667
38   16.46666667   12.35   28.18333333

Thus, as

chi^2 = Sum[(O - E)^2/E]

Then

chi^2 = 5.887309817

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,

a =    4
b =    2
  
df =    3

Thus, getting the p value by technology,

p = 0.117223434

As p > 0.01, we fail to reject the null hypothesis.

THAT MEANS WE HAVE NO SUFFICIENT EVIDENCE THAT THE CHOICE OF MAJOR IS DEPENDENT ON GENDER.