Question

This question is an extension from Q2 above. The high school teacher was also interested in whether there is a gender difference in terms of the student’s choice of majors. So he broke the data down by gender in the following table and conducted a Chi-square test for independence with α = .05.

Type of Major	Female	Male	Total
STEM	10	25	35
Social Sciences	11	9	20
Liberal Arts	7	3	10

a. What are the variables in this analysis? What scale of measurement is each variable (nominal, ordinal, or continuous)? (2 points total: 1 for each variable- .5 for variable name, .5 for variable type)

b. State the null and alternative hypotheses in words (1 point total: .5 for each hypothesis)

c. Calculate X2 statistic (2 points total: 1 for final answer, 1 for the process of calculating it)

d. Calculate the degree of freedom and then identify the critical value (1 point total: .5 for df, .5 for critical value)

e. Compare the X2 statistic with the critical value, then report the hypothesis test result, using “reject” or “fail to reject” the null hypothesis in the answer (1 point total, .5 for each answer)

f. Explain the conclusion in a sentence or two, to answer the research question. (1 point)

Answer 1

a)

The variables and in this analysis with the types of measurement are :

Type of Major: Nominal

Gender: Nominal

b)

Null hypothesis: There is no association between type of major and gender.

Alternative hypothesis: There is an association between type of major and gender.

c)

To compute chi square test statistic:

Sum of w-values of all the cells (2X3=6)

Where w value for (i,j) cell is [(O(i,j) – E(i,j))^2]/E(i,j)

Where O (i,j) is observed frequency and E (i,j) cell is T(i) X T(j) /n

T(i): total for row i and T(j) Total for column j

N=sum of values in all the cells

For example, w(1,1)=(10+11+7)*(10+25) /(35+20+10)

Similarly computing all such values and summing them, we get

Chi square statistic (S) = 7.119

d)

The degrees of freedom are (3-1)*(2-1) = 2*1=2

Thus the critical value at alpha=0.05 is 5.99

e)

Since the test statistic is greater than critical value, the null hypothesis is rejected.

f)

It seems based on the given data that there is an association between the major type and gender.