Question

12.14.  A random sample of 100 men and 100 women were asked whether they would be willing to work as unpaid volunteers. The results indicate that 54% of the men and 64% of the women responded YES to this question, while 46% of the men and 36% of the women responded NO to the question. The chi square test was used to determine whether the men and women in the study differ in their willingness to work as unpaid volunteers. The obtained chi square value was 2.06 (c²_(obt)=2.06). The appropriate critical value at p=.05 is 3.841 (c²_{crit (.05)}=3.841).

a.         Which chi square test was used to analyze the data and determine whether there are gender differences between the responses of the men and women who participated in the survey? Explain.

b.             What was the null hypothesis for the study?

c.             Was there a gender difference between the responses of the male and female participants? Explain.

Answer 1

a - ::

Since it is an attribute of a population that is under study, and rather there are proportions considered, here chi square test for independence of attributes is used, rather but here in our case, we would like to call it chi square test for testing difference in proportions of male and females responses for unpaid volunteering. Explanation of above can be done as:

If we consider proportion of responses for unpaid volunteering as random variable, then this random variable should take value same, whether we go in male group or we go in female group. Therefore we consider this testing as testing of equality of proportions while it is basically same as testing of attributes.

b-::

Null hypothesis is "there is no gender difference bwtween the responses of male and female participants".

c-::

Since obtained chi square is less than critical chi square, therefore there is not much evidence to reject the null hypothesis at . 05 level of significance, hence we find there is not significant gender difference bwtween the responses of males and female participants .