Question

2. A prospective college student was interested in whether the school he had chosen to attend was as racially diverse as the three-county region surrounding it. He found census data and school data regarding the racial diversity of the counties and the university. The census data indicated that the region was 15 percent Asian, 48 percent black, and 37 percent white. Assume that the accepted freshman class at the target university totals 1042 and that 729 students self-identify as white, 202 as black, and 111 as Asian. Perform steps 4 through 6 of hypothesis testing to determine whether the distribution of students at this university reflects the racial diversity of the region. You may use excel to calculate chi-square.

Step 4: The critical value based on a p level of 0.05 and df = 2 is ____________

Step 5: χ² =__________

Step 6: Decision:

Answer 1

Category	Observed (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
Asian	111	0.15	1042 * 0.15 = 156.3	(111 - 156.3)²/156.3 = 13.1292
Black	202	0.48	1042 * 0.48 = 500.16	(202 - 500.16)²/500.16 = 177.7419
White	729	0.37	1042 * 0.37 = 385.54	(729 - 385.54)²/385.54 = 305.9728
Total	1042	1.00	1042	496.8439

Critical value:

χ²α = CHISQ.INV.RT(0.05, 2) = 5.991

Test statistic:

χ² = ∑ ((O-E)²/E) = 496.844

df = n-1 = 2

Decision:

p-value < α, Reject the null hypothesis.

The distribution of students at this university does not reflects the racial diversity of the region.