A random group of students was asked to name their favorite type of music. The c

Question

A random group of students was asked to name their favorite type of music. The campus, radio station believes that 18% of the students prefer rap, 22% prefer rock, 15% prefer country, 17% prefer new age, and 28% prefer oldies. Is there evidence to reject this hypothesis at = 0.05? There is not evidence to reject the claim that the favorite music types are distributed is claimed because the test value 9.488 > 7.240 There is evidence to reject the claim that the favorite music types are distributed as claimed because the test value 7.240 7.240

Explanation / Answer

Solution

Let Oi and Ei be respectively the observed (given) and

expected frequency in the ith class.

Then, Ei = n x pi, where pi = expected probability

which is estimated by proportion or percentage in the ith class

Claim: Favourite music types are as claimed by campus radio station.

Hypotheses:

Null H0: Distribution of Favourite music types is as claimed by campus radio station

Vs

Alternative HA: H0 is false.

Test statistic:

2 = [1,5]{(Oi - Ei)2/Ei}.

Computations

Class i

1

2

3

4

5

Total

Oi

21

25

19

18

16

99

pi

0.18

0.22

0.15

0.17

0.28

1

Ei

17.82

21.78

14.85

16.83

27.72

99

Chi-square

0.567475

0.476051

1.159764

0.081337

4.955209

7.239837

CHECK: sumOi must equal sumEi.

Done.

Chi-square =

7.23983

Distribution, Critical Value

Under H0, 2 ~ 2n – 2, where n = number of classes = 5.

Critical value = upper % point of 2n – 2.

Given = 0.05, 2crit= 23, 0.05= 7.815.

Decision Criterion (Rejection Region)

Reject H0, if 2cal > 2crit

Decision:

Since 2cal < 2crit, H0 is accepted.

Conclusion:

There is sufficient evidence to support the claim that the Favourite music types are as claimed by campus radio station. Or, put in a different way but meaning the same, ‘There is not sufficient evidence to reject the claim that the Favourite music types are as claimed by campus radio station.’ Second Option

DONE

Let Oi and Ei be respectively the observed (given) and

expected frequency in the ith class.

Then, Ei = n x pi, where pi = expected probability

which is estimated by proportion or percentage in the ith class

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