Question

A student wants to see if the correct answers to multiple choice problems are evenly distributed. She heard a rumor that if you don't know the answer, you should always pick C. In a sample of 89 multiple-choice questions from prior tests and quizzes, the distribution of correct answers are given in the table below. In all of these questions, there were four options {A, B, C, D}.

Correct Answers (?=89)

n

=

89

)

A B C D

Count 23 22 34 10

Test the claim that correct answers for all multiple-choice questions are not evenly distributed. Test this claim at the 0.10 significance level.

(a) Find the test statistic.

(b) Find the critical value.

(c) Is there sufficient data to support the claim?

Yes

No

Answer 1

Answer :

Given data is :

Sample size n = 89

A	B	C	D
23	22	34	10

Based on these,

Null hypothesis is :

Correct answers for all multiple choice questions are evenly distributed.

Alternative hypothesis is ;

Correct answers for all multiple choice questions are evenly distributed.

Now,

Choice	Probability (P)	Observed (O)	Expected value (E) E = n * p
A	1 / 4 = 0.25	23	= 89 * 0.25 = 22.25	= = = =0.0253
B	1 / 4 = 0.25	22	22.25	0.0028
C	1 / 4 = 0.25	34	22.25	6.205
D	1 / 4 = 0.25	10	22.25	6.744
		= 23 + 22 + 34 +10 = 89		= 0.0253 + 0.0028 + 6.205 + 6.744 = 12.977

a)Test statistics = 12.977

b)Given significance level

Degree of freedom df = n - 1 = 4 - 1 = 3,

So critical value form chi square table is ;

Critical value = 6.251.

We get Critcal value < test statistics.

c)YES

We have sufficient evidence to support the claim.