Question

Is achieving a basic skill level related to the location of the school? The results of a random sample of students by the location of Subject school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At a = 0.05, test Location Reading Math Science the hypothesis that the variables are independent. Complete parts (a) through (d). Urban 49 42 43 Suburban 69 64 62 (a) Identify the claim and state the null and alternative hypotheses. Ho: Skill level in a subject is location He: Skill level in a subject is location The is the claim (b) Calculate the test statistic. If convenient, use technology (Round to three decimal places as needed.) (c) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Choose the correct conclusion below. O A. Fail to reject the null hypothesis. There is not enough evidence to reject OB. Reject the null hypothesis. There is not enough evidence to reject the the claim that skill level in a subject is independent of location. claim that skill level in a subject is independent of location. OC. Reject the null hypothesis. There is enough evidence to reject the claim OD. Fail to reject the null hypothesis. There is enough evidence to reject the that skill level in a subject is independent of location. claim that skill level in a subject is independent of location.

Answer 1

#Given that it subject Total science Location Math Reading 49 Urban 42 43 134 sub Urban 69 64 62 195 Total 118 106 105 329 a) Hypothesis testing : Ho: Skill level in a subject is independent) to location Hi: Skill level in a subjet is not independent of location. The skill level in a subject is independent of location is the claim. b) Expected frequency (ei) = Row Sum x Column Sum Grand Total E(49) = 134 x118 = 48.061 E(69) = 195x118 = 69.939 329 329 El 42 ) - 134 x 106 = 43.173 E[64) = 195x106 = 62.827 329 329 42:766 E[62) - 195x105 = 62.234 E[ 43) = 134 x105 329 329 Observed Expected (0;-&13/1 (Oi) CE) 0.018 - 48-061 49 0.032 43.173 u2 43 42.766 0.001 69 69.939 0.013 67 0,022 62.827 0.001 62 62 234 Totat 0.007

x² = E (Oireid? - 10.007 ~ Tood7 Ei c) degree of freedom (d.f)= (-1) (C-1) = (2-1)(3-1)=) 142 = 2 Q = 0.05 Cgiven) S.991 Car,df) critical value x2 = x araty = 8 8.05, 20- (from chi-square table) Xox xe: Hence Accept the will Hypothesis (HO) so we conclude that Fail to reject Ho, there is not enough evidence to reject the claim that skill level in a subject is independent of location.