Question

120 students who were majoring in math or english were asked a test question, and the researcher recorded wheter they answered the question correctly. the sample results are given below. at the 0.05 significance level, test the claim that response and major are independent. correct incorrect math 24 46 english 35 15 what is a. claim, b. test statistics, c. critical values d comparison between test statistics and critical value, and e. conclusion.

Answer 1

Answer :

Given that :

No.of students = 120

= 0,05

Math	24	46
English	35	15

a)Claim :

Null hypothesis :

$H_{0}$ : The responses are independent of majors

Alternative hypothesis :

$H_{1}$ : The responses are not independent of major

b)Here we are applying chi-square test :

Math	24	46	70
English	35	15	50
Total	= 24 + 35 = 59	= 46 + 15 = 61	120

therefore,

Grand total = 120

Observations	Expected frequency (E)	(0 - E)/E
24	= (70*59)/120 = 4130 / 120 = 34.42	= (24-34.42)2/34.42 = 3.15
46	= (70 * 61) / 120 = 35.58	= (46 - 35.58)2/35.58 = 3.05
35	= (50 * 59) / 120 = 24.58	4.41
15	= (50 * 61) / 120 = 25.42	4.27

Σο - Ε)? /Ε

= 3.15 + 3.05 + 4.41 + 4.27

= 14.89

x2 = 14.89

c)From chi square value ,

critical value of $\chi^2$ = 3.84

Where df = (row - 1)(column - 1) = (2 - 1)(2 - 1) = 1

= 0,05

d)Here $\chi^2$ > Critical value

i.e 14.89 > 3.84

So null hypothesis is rejected.

e)Based on these values,there is no sufficient evidence that the response are independent of majors.