Question

A spinner mounted in the center of a piece of circular cardboard that is divided into five areas of equal size. Each of the five areas is a different color (pink, orange, blue, purple, green). Joy suspects that the spinner is defective because he keeps landing on pink. The spinner is spun 50 times. The results are shown below.

Color	Pink	Orange	Blue	Purple	Green
Frequency	8	11	14	8	9

Test Joy's claim that the spinner is in fact defective. Use the α = 0.05 level of significance. You must show all of these steps.

a) State the null and alternative hypotheses.

b) Give the P −value. Round to the nearest ten-thousandth (4 decimal places).

c) Test the hypothesis at the α = 0.05 level of significance.

d) State the conclusion in a sentence.

Answer 1

a).hypothesis:-

the proportion of landing on each colored area is equal, i.e , 1/5 = 0.20

at least one of the area has different proportion (i.e, the spinner is defective )

b).the necessary calculation table :-

color	observed	expected
pink	8	50*0.2 = 10	(8-10)2/10 = 0.4
orange	11	10	0.1
blue	14	10	1.6
purple	8	10	0.4
green	9	10	0.1
	sum = 50		sum=2.6

the test statistic be:-

c). df = (5-1) = 4 [ as there are five colors ]

the p value = 0.6268

[ in any blank cell of excel type =CHISQ.DIST.RT(2.6,4) ]

d).decision:-

p value = 0.6268 > 0.05 (Alpha)

we fail to reject the null hypothesis.

e).conclusion:-

there is not enough evidence to support Joy's claim that the spinner is in fact defective.

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