Question

1) Previous enrollment records at a large university indicate that of the total number of students who apply for admission, 60% are admitted unconditionally, 5% are admitted on a trial basis, and the remainder were refused admission. Of 500 applicants to date for the coming year, the following counts were observed: Status: Number: Admitted unconditionally 329 Trail basis 43 Refused admission 128 At the 0.05 significance level, test the claim that the to-date data indicate a departure from the previous admission rates. (a) State the null and alternative hypothesis. (b) Find and label the observed frequencies and the expected frequencies. (c) The test statistic is x2 = 28.39. Perform the test and state the specific conclusion for this problem.

Answer 1

a).hypothesis:-

$H_{0}:p_{admitted}=0.60,p_{trail}=0.05,p_{refused}=0.35$[ as, 1-(0.60+0.05)=0.35 ]

b). the observed and expected table be:-

status	observed	test proportion	expected
admitted unconditionally	329	0.60	500*0.60= 300
trail basis	43	0.05	500*0.05 = 25
refused admission	128	0.35	500*0.35 = 175
	sum = 500

c). test statistic is :-

x = 28.39

df = (3-1) = 2

p value = 0.0000

[ in any blank cell of excel type =CHISQ.DIST.RT(28.39,2) ]

decision:-

p value = 0.0000< 0.05 (alpha)

we reject the null hypothesis. There is sufficient evidence to claim that the to date data indicate a departure from the previous admission rates.

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