Question

Your statistics professor’s favorite coffee merchant always throws in a small sample of a flavored black coffee when they ship an order to her. Her friend who works there assures her that the coffee samples have always been 45% fruit teas, 20% spice teas, and 35% Earl Greys.4 When your statistics professor tracks the samples she receives over the course of several years, she finds that she has received 13 fruit tea samples, 5 spice tea samples, and 8 Earl Grey samples. Test the hypothesis that her friend’s proportions are accurate at a significance level of α = .05.

Answer 1

necessary calculation table:-

coffee samples	observed	test proportion	expected
fruit teas	13	0.45	26*0.45 = 11.7	(13-11.7)2 /11.7 = 0.14444
spice teas	5	0.20	26*0.20 = 5.2	0.00769
Earl Greys	8	0.35	26*0.35 = 9.1	0.13297
total	26			sum= 0.2851

hypothesis:-

at least one of the proportions are different than expected.

test statistic is:-

df = (3-1) = 2

the p value = 0.8671

[ in any blank cell of excel type =CHISQ.DIST.RT(0.2851,2)]

decision:-

p value = 0.8671 > 0.05 (alpha)

we fail to reject the null hypothesis and conclude that there is enough evidence to claim that her friend’s proportions are accurate at a significance level of α = 0.05.

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