A manufacturer of floor polish conducted a consumer-preference experiment to det
ID: 3153348 • Letter: A
Question
A manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance. A sample of 100 consumers viewed five patches of flooring that had each received one of the five polishes. Each consumer indicated the patch he or she preferred. The lighting and background were approximately the same for all patches. The results are given below. Solve the following using the p-value approach and solve using the classical approach.
(a) State the hypothesis for "no preference" in statistical terminology.
(b) What test statistic will be used in testing this null hypothesis?
(c) Complete the hypothesis test using = 0.10.
(i) Find the test statistic. (Give your answer correct to two decimal places.)
(ii) Find the p-value. (Give your answer bounds exactly.)
< p <
(iii) State the appropriate conclusion.
Explanation / Answer
a)
H0: P(A) = P(B) = P(C) = P(D) = P(E) = 0.2 [ANSWER]
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b)
As this is a goodness of fit, we use 2. [ANSWER]
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c)
i.
Doing an observed/expected value table,
O E (O - E)^2/E
22 20 0.2
17 20 0.45
17 20 0.45
21 20 0.05
23 20 0.45
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 1.6 [ANSWER, TEST STATISTIC]
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ii.
As df = a - 1,
a = 5
df = a - 1 = 4
Hence, the p value is, using tables,
0.20 < P < 1 [ANSWER]
[The exact P value using technology is 0.8087. Please use the bounds you use in class.]
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iii.
As P is very large, we
OPTION B: Do not reject H0. There is no evidence of a consumer preference. [ANSWER, B]
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