Question

The value of a college degree is greater than it has been in nearly half a century, a least when compared to the prospect of not getting a degree (www.pewresearch.org, January 28, 2014). Due to this fact, more and more people are obtaining college degrees, despite the soaring costs. The accompanying table shows the proportions of college degrees awarded in 2010 by colleges and universities, categorized by a graduate's race and ethnicity.

The race and ethnicity of 500 recent graduates are recorded and shown in the last column of the table.

Race/Ethnicity	2010 Proportions	Recent Numbers
White	0.73	350
Black	0.10	50
Hispanic	0.09	60
Asian	0.08	40

At the 5% significance level, test if the proportions have changed since 2010.

Answer 1

The expected frequency for each category here is computed as:

proportion of category*500 because 500 is total frequency here.

The chi square test statistic value here is computed as:

Race	2010 Proportion	O_i	E_i	(O_i - E_i)^2/E_i
White	0.73	350	365	0.616438356
Black	0.1	50	50	0
Hispanic	0.09	60	45	5
Asian	0.08	40	40	0
				5.616438356

From the above table, last column, we get the required test statistic value here as:

Degrees of freedom = n - 1 = 3

Therefore the p-value here is computed from the chi square distribution tables as:

As the p-value here is 0.13 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence to reject the claim that the proportions are like the 2010 today as well.