Question

In an effort to get a better understanding of the factors affecting a high school student choice of college selection, 600 students were reported to apply for college admission from Sacramento county and they were asked to provide information on SAT scores and parent’s income. Portion of that data is reported in the table below. Use Chi-square test to examine how the categorical variable parent’s income affects the choice of professional degree among those who have applied for admission. Run the Chi square test and answer the three parts.

Income Attribute	Liberal Arts	Business Administration	Law and Engineering	Total
<65,000	67	38	55	160
65,001-90,000	35	88	67	190
90,001>	33	177	40	250
Total	135	303	162	600

1. Write the null and alternative hypothesis
2. Determine the P value and provide its interpretation
3. What is your conclusion after running the Chi square test?

Income	University Choice	Count
less than 65000	CSU Sacramento	67
65001 to 90,000	CSU Sacramento	35
90001 and above	CSU Sacramento	33
less than 65000	UC Davis	38
65001 to 90,000	UC Davis	88
90001 and above	UC Davis	177
less than 65000	San Francisco Univ	55
65001 to 90,000	San Francisco Univ	67
90001 and above	San Francisco Univ	40

Answer 1

Observed Frequencies
	Liberals arts	Business adm.	Law & Eng.	Total
<65000	67	38	55	160
65001-90000	35	88	67	190
90001>	33	177	40	250
Total	135	303	162	600
Expected Frequencies
	Liberals arts	Business adm.	Law & Eng.	Total
<65000	135 * 160 / 600 = 36	303 * 160 / 600 = 80.8	162 * 160 / 600 = 43.2	160
65001-90000	135 * 190 / 600 = 42.75	303 * 190 / 600 = 95.95	162 * 190 / 600 = 51.3	190
90001>	135 * 250 / 600 = 56.25	303 * 250 / 600 = 126.25	162 * 250 / 600 = 67.5	250
Total	135	303	162	600
	(fo-fe)²/fe
<65000	(67 - 36)²/36 = 26.6944	(38 - 80.8)²/80.8 = 22.6713	(55 - 43.2)²/43.2 = 3.2231
65001-90000	(35 - 42.75)²/42.75 = 1.405	(88 - 95.95)²/95.95 = 0.6587	(67 - 51.3)²/51.3 = 4.8049
90001>	(33 - 56.25)²/56.25 = 9.61	(177 - 126.25)²/126.25 = 20.4005	(40 - 67.5)²/67.5 = 11.2037

a) Null and Alternative hypothesis:  

Ho: Parent's income does not affect the choice of professional degree.

H1: Parent's income does affect the choice of professional degree.

b) Test statistic:  

χ² = ∑ ((fo-fe)²/fe) =    100.6716

df = (r-1)(c-1) =    4

p-value = CHISQ.DIST.RT(100.6716, 4) = 0.000

c) Decision:  

p-value < 0.05, Reject the null hypothesis.  

There is enough evidence to conclude that Parent's income does affect the choice of professional degree.