Question

160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent.

	Correct	Incorrect
Math	27	53
English	43	37

Fill in the blanks

Ho:

H1:

Test statistic . Round your answer in 4 decimal places.

Critical value . Round your answer in 2 decimal places.

Decision

A) Reject the Ho.

B) Do not reject the Ho

Type A or B in the box

Conclusion:

A) The response and major are independent.

B) The response and major are dependent.

Type A or B in the box

Answer 1

		Correct	Incorrect	Total
Math	Observed	27	53	80
	Expected	35.00	45.00	80.00
	(O - E)² / E	1.83	1.42	3.25
English	Observed	43	37	80
	Expected	35.00	45.00	80.00
	(O - E)² / E	1.83	1.42	3.25
Total	Observed	70	90	160

To Test :-

H0 :-  Response and major are independent

H1 :-  Response and major are dependent

Test Statistic :-
= Σ (Oi - Ei )2 / Ei
= 6.5016

Critical value X2(0.1,1) = 2.71 ( From chi square table ))

Test Criteria
Reject null hypothesis if > (α,(c-1))
Since, 6.5016 > 2.71
Conclusion = Reject null hypothesis

A) Reject the Ho.

B) The response and major are dependent.