Question

The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table (below). Complete the table and decide to accept/reject. Discuss why. Denied Admitted Wait List 45 21 33 13 Urban Rural Suburban Other 17 24 39 34 12 19 7 22

Answer 1

The Excel output is:

R28 fi X A - B D G H K E Total 1 Observed 2 45 21 17 83 3 33 13 24 70 fo-fe 6.982517 5.618881 -12.6014 0.937063 0.027972 -0.96503 -4.93357 -3.75175 8.685315 -2.98601 -1.8951 4.881119 4 34 12 39 85 19 7 22 48 131 53 102 286 5 6 Total 7 8 9 10 Expected Total 38.01748 15.38112 29.6014 83 32.06294 12.97203 24.96503 70 38.93357 15.75175 30.31469 85 21.98601 8.895105 17.11888 48 131 53 102 286 (fo-fe)^2/fe 1.282451 2.052635 5.364451 0.027386 6.03E-05 0.037304 0.625169 0.893591 2.488388 0.405543 0.403753 1.391757 11 12 13 Total 14 15 16 Level 17 R 0.05 4 3 18 C 19 DF 6 20 12.59159 21 CV 22 X2 14.97249 0.020472 23 P-value 24 2

The Excel formulas are:

R28 X A B C D E F Н 1 2 45 17 3 33 24 Observed 21 13 12 7 =SUM(C2:C5) Total =SUM(B2:D2) =SUM(B3:D3) =SUM(B4:04) =SUM(B5:05) =SUM(B6:06) fo-fe =B2-B9 =B3-B10 =B4-B11 =B5-B12 =C2-C9 =C3-C10 =C4-C11 =C5-C12 =D2-09 =D3-D10 =D4-D11 =D5-012 4 34 39 5 19 22 =SUM(D2:05) 6 Total =SUM(B2:35) 7 8 9 10 =($B$6*E2)/$E$6 =($B$6*E3)/$E$6 =($B$6*E4)/$E$6 =($B$6*55)/$E$6 =SUM(B9:B12) Expected =($C$6*E2)/$E$6 =($C$6*E3)/$E$6 = ($C$6*E4)/$E$6 =($C$6*E5)/$E$6 =SUM(C9:012) = ($D$6*E2)/$E$6 =($D$6*E3)/$E$6 =($D$6*E4)/$E$6 = ($D$6*E5)/$E$6 =SUM(D9:012) Total =SUM(B9:09) =SUM(B10:010) =SUM(B11:011) =SUM(B12:012) =SUM(B13:013) (fo-fe)^2/fe =(G2*G2)/B9 =(G3*G3)/B10 =(G4*G4)/B11 =(G5*65)/B12 = (H2*H2)/C9 =(H3*H3)/C10 = (H4*H4)/C11 =(H5*H5)/012 = (12*12)/D9 = (13*13)/D10 = (14*14)/D11 = (15*15)/012 0.05 12 13 Total 14 15 16 Level 17 R 18 C 19 DF 20 21 CV 4 3 6 22 XP 23 P-value 24 =CHISQ.INV(1-B16,819) =SUM(G9:112) =CHISQ.DIST.RT(B22,819)

The answer is:

		Observed	Total		fo - fe
	45	21	17	83		6.982517	5.618881	-12.6014
	33	13	24	70		0.937063	0.027972	-0.96503
	34	12	39	85		-4.93357	-3.75175	8.685315
	19	7	22	48		-2.98601	-1.8951	4.881119
Total	131	53	102	286
		Expected		Total		(fo - fe)^2/fe
	38.01748	15.38112	29.6014	83		1.282451	2.052635	5.364451
	32.06294	12.97203	24.96503	70		0.027386	6.03E-05	0.037304
	38.93357	15.75175	30.31469	85		0.625169	0.893591	2.488388
	21.98601	8.895105	17.11888	48		0.405543	0.403753	1.391757
Total	131	53	102	286
Level	0.05
R	4
C	3
DF	6
CV	12.59159
X²	14.97249
P-value	0.020472

Since the p-value (0.020472) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that admission status is not independent of the type of community in which an applicant resides.