Question

In: Statistics and Probability

160 students who were majoring in either math or English were asked a test question, and...

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

Solutions

Expert Solution

Answer:

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.

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