Question

A one pound gold-plated tin of Almas caviar costs $12,000. In a blind taste test, 212 food experts tasted four premium caviars, with the most expensive caviar being Almas. Each taster was asked to select the Almas and the observed outcomes are below.

Observed outcomes: Brand A: 10, Brand B: 18,  Brand C: 34, Almas: 140

Do a goodness-of-fit analysis to test the hypothesis that the distribution of the responses is not typical (that is to say, tasters could tell the difference). Ho: _________________________________________________________________ Ha: _________________________________________________________________ df = __________ X squared = _________ 0.05= significance level p = ___________

Circle one: Fail to Reject Ho OR Reject Ho

Conclusion: __________________________________________________________ ____________________________________________________________________

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
A	10	0.25	202 * 0.25 = 50.5	(10 - 50.5)²/50.5 = 32.4802
B	18	0.25	202 * 0.25 = 50.5	(18 - 50.5)²/50.5 = 20.9158
C	34	0.25	202 * 0.25 = 50.5	(34 - 50.5)²/50.5 = 5.3911
Almas	140	0.25	202 * 0.25 = 50.5	(140 - 50.5)²/50.5 = 158.6188
Total	202	1.00	202	217.4059

Null and Alternative hypothesis:  

Ho: Proportions are same.  

H1: Proportions are different.  

Test statistic:  

χ² = ∑ ((O-E)²/E) =    217.4059

df = n-1 =    3

p-value = CHISQ.DIST.RT(217.4059, 3) = 0.000   

Decision:  

p-value < α, Reject the null hypothesis  

There is enough evidence to conclude that the distribution of the responses is not typical that is the tasters could tell the difference at 0.05 significance level.