Question

in a 2012 report from the u.s. department of education breaking down the race and gender of every u.s. college graduate receiving a bachelors degree in 2009 - 2010, we see the following data for white, black, and hispanic graduates. (numbers are in 1000s.)
source: \degrees conferred by sex and race,\ national center for education statistics, u.s. department of education. https://nces.ed.gov/fastfacts/display.asp?id = 72
the expected count of hispanic males receiving a bachelors degree is the number of students that you would expect to see assuming that which of the following is correct? check all that apply.
a. the conditions that allow us to safely use the chi - squared procedure are met.
b. race and gender are related.
c. the sample is large enough.
d. the null hypothesis of the chi - squared test for independence in this case is true.

Explanation:

• Option A: The expected count is calculated under the assumption that the conditions for the chi - squared procedure (such as independence of observations, etc.) are met. But this is more about the validity of the test rather than the direct assumption for calculating the expected count.
• Option B: If race and gender were related, we would not be calculating the expected count under an assumption of independence. So this is incorrect.
• Option C: The sample size being large enough is a condition for the validity of the chi - squared test (like having expected counts not too small), but it is not the assumption for calculating the expected count itself.
• Option D: The formula for the expected count \(E_{ij}=\frac{R_i\times C_j}{n}\) (where \(R_i\) is the row total, \(C_j\) is the column total and \(n\) is the grand total) is derived under the null hypothesis of independence (i.e., the null hypothesis of the chi - squared test for independence is True).

Answer:

D. The null hypothesis of the chi - squared test for independence in this case is true.