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 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.

Polish A B C D E Total Frequency 29 15 16 21 19 100

(a) State the hypothesis for “no preference” in statistical terminology. H0: P(A) ≠ P(B) ≠ P(C) ≠ P(D) ≠ P(E) H0: P(A) + P(B) + P(C) + P(D) + P(E) = 1 H0: P(x) = P(y) for some x and y H0: P(A) = P(B) = P(C) = P(D) = P(E) = 0.2

(c) Complete the hypothesis test using α = 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. Reject H0. There is significant evidence of a consumer preference. Do not reject H0. There is no evidence of a consumer preference.

A manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance.