Question

39 2. is achieving a basic skill level related to the location of the Subject school? The results of a random sample of students by the Location Reading Math Science location of school and the number of students achieving Urban 45 49 basic skill levels in three subjects is shown in the Suburban 69 contingency table. At a = 0.05, test the hypothesis that the variables are independent. Complete parts (a) through (d). (a) Identify the claim and state the null and alternative hypotheses. Ho: Skill level in a subject is (1). location Hg: Skill level in a subject is (2) location. The (3) - is the claim. (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? d.f. = Find the critical value. x = (Round to three decimal places as needed.)

Answer 1

Ans.

(a) Hypothesis:-

H0 : Skill level in a subject is independent of location.

H1 : Skill level in a subject is dependent on location.

The null hypothesis is claim.

(b) l = 2 , k = 3

df = (l-1)(k-1) = (2-1)(3-1) = 2

df = 2

Critical Value:-

$\alpha= 0.05, df=2$

$\chi^2_{0}=5.991\;\;(from \;\chi^2\;table)$

Rejection Region:-

$\chi^2>\chi^2_{0}$

(c). We find test statistics using MINITAB:-

Steps:-

1    Choose Stat > Tables > Chi-Square Test (Table in Worksheet).

2    In Columns containing the table, enter the columns containing the contingency table data. Click OK.

Chi-Square Test: Reading, Math, Science Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Urban Reading Math Science Total 4549 39 133 46.09 45.28 41.64 0.026 0.306 0.167 Sunurban 64 196 6963 67.91 66.72 0.017 0.208 61.36 0.113 Total 114 112 103 329 Chi-sq - 0.837, DF = 2, P-Value = 0.658

$\chi^2=0.837$

(d). Decision:-

$Since,\;\chi^2=0.837< \chi^2_{0}=5.991$

$Hence,\;we;fail\;to\;reject\;H_{0}\;at\;\alpha=0.05$

Fail to reject the null hypohesis. There is not enough evidence to reject the claim that skill level in subject is independent of location.