A random sample of Canadian university undergraduate student

A random sample of Canadian university undergraduate students was given a questionnaire designed to find out whether they would consider seeking a graduate degree. Male and female students were questioned and their responses were as follows:

At = .05, test the hypothesis that the decision to pursue a graduate degree is independent of sex for these university students.

Solution

COntructing an observed value table,

Pursue a Grad Degree   Male   Female
Yes   82.5   117.5
No   82.5   117.5

Thus, using

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

Then

chi^2 = 0.505480335

As

df = (a - 1)(b - 1)

where a and b are the categories for each variable, and a = b = 2 here, thus, the p value is

p = 0.477101957

The critical chi squared value also is

chi^2 (crit) = 3.841458821

Thus, by the p value and critical value [p > 0.05, chi^2 < chi^2 (crit)], we fail to reject the null hypothesis.

There is insufficient evidence that pursuing a graduate degree is dependent of sex.