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
what is the chi - squared statistic for this data?
a. 3.81
b. 2.80
c. 6.63
d. 2.06

Explanation:

Step1: Calculate the chi - squared statistic for each cell

The formula for the chi - squared statistic for a cell is \(\chi^{2}=\sum\frac{(O - E)^{2}}{E}\), where \(O\) is the observed value and \(E\) is the expected value.
For white males: \(\frac{(514 - 508.32)^{2}}{508.32}=\frac{5.68^{2}}{508.32}=\frac{32.2624}{508.32}\approx0.0635\)
For white females: \(\frac{(654 - 689.68)^{2}}{689.68}=\frac{(- 35.68)^{2}}{689.68}=\frac{1272.9424}{689.68}\approx1.846\)
For black males: \(\frac{(56 - 70.01)^{2}}{70.01}=\frac{(-14.01)^{2}}{70.01}=\frac{196.2801}{70.01}\approx2.804\)
For black females: \(\frac{(109 - 94.99)^{2}}{94.99}=\frac{14.01^{2}}{94.99}=\frac{196.2801}{94.99}\approx2.066\)
For Hispanic males: \(\frac{(55 - 59.40)^{2}}{59.40}=\frac{(-4.4)^{2}}{59.40}=\frac{19.36}{59.40}\approx0.326\)
For Hispanic females: \(\frac{(85 - 80.60)^{2}}{80.60}=\frac{4.4^{2}}{80.60}=\frac{19.36}{80.60}\approx0.240\)

Step2: Sum up the values

\(\chi^{2}=0.0635 + 1.846+2.804+2.066+0.326+0.240\approx7.345\) (There might be some calculation errors due to approximation in each step. Let's recalculate more accurately)

Another way:

$$
LATEXBLOCK0
$$

Answer:

C. \(6.63\)