Question

is achieving a basic level related to the location of the school? The results of a random sample of students by the location of school and the number of students achieving basic levels in three subject is shown in the contingency table. Ata 0.05. test the hypothesis that the variables are independent. Complete parts (a) through (d) Subject Location Reading Math Science Urban 4 47 32 Suburban 61 82 55 The ruil hypothesis is the claim 0) Determine the degree of freedom, find the critical value, and identify the rejection region What are the degrees of freedom? d. 2 Find the critical value (Round to three decimal places as needed) Choose the correct rejection region below. (c) Calculate the best statistici convenients technology (Round to the decimal places as needed)

Answer 1

Chi- square test of independence:

Test of Independence Statistic for chi-sq. Test given РЯ is 2. й &. ( fiij- eij eij анализ where tii Obseened to iti sol & ith Colunm corresponding мара ча corresponding eij • Expected to pri socor Column. --- follows x²-variale with (-1) (s- 1) reedom. freedom number ol и и040 jous num в Column. %

Now or eij is computed by eijs = Ri xej where ith row Ri total sum of 0 total Sum c of ith column total Cerand T

. -Test Statistic x SE C fij - ei;)? eig

	Reading	Math	Science	Total
Urban	48	47	32	127
SubUrban	61	62	55	178
Total	109	109	87	305

Expected frequency table. Suence. Reading Math - 36.23 127 x 87 Vobon 45.39 127-4109, = 45.39 30s 129 X 109 305 305 178% 87 Suburban = 50.27 178 X 109 = 63.61 178x169 = 63.61 305 305 305 squared distance table. Math Science. Reading 2 (48-45.39) - 0.15 (44-4539) - 0:49 (32-36-23) 0.06 Urban 45.39 36.25 US.39 (61-63.61) Suburbon (55-50.72) = 0.35 = 0.11 (62-63-61)?= 0.04 63.61 63.61 So.77 There fore, to ou to-35 0.15 + 0.49 + 0.11 + 0.06 1.201 X = 1.2008