Question

Is gender independent of education level? A random sample of 395 people were
surveyed and each person was asked to report the highest education level they
obtained. The data that resulted from the survey is summarized in the following table:
High School Bachelors Masters Ph.d. Total
Female 60 54 46 41 201
Male 40 44 53 57 194
Total 100 98 99 98 395
Question: Are gender and education level dependent at 5% level of significance? In
other words, given the data collected above, is there a relationship between the
gender of an individual and the level of education that they have obtained?

Answer 1

Here we are to perform chi square test of indepenence

The null and the alternative hypotheses are given by

H₀:Gender of an individual and the level of education that they have obtained are independent

against

H₁: Gender of an individual and the level of education that they have obtained are not independent

Now we make a table

	High School	Bachelors	Masters	PhD	Total
Female	60	54	46	41	n1=201
Male	40	44	53	57	n2=194
Total	f01=100	f02=98	f03=99	f04=98	n=395

The test statistic is given by

where f_ij is the observed frequency of the i-th row and j-th column

The test statistic follows chi square distribution with df 3.

The p-value is obatined as 0.045883

As the p-value is less than 0.05, we reject the null hypothesis at 5% level of significance and hence conclude that there is statistically significant relationship between gender of an individual and the level of education that they have obtained

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