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.

Polish	A	B	C	D	E	Total
Frequency	26	18	14	21	21	100

(a) State the hypothesis for "no preference" in statistical terminology.

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) H₀: P(A) = P(B) = P(C) = P(D) = P(E) = 0.2

(b) What test statistic will be used in testing this null hypothesis?

χ²t     p μ z

(c) Complete the hypothesis test using α = 0.10.
(i) Find the test statistic. (Round your answer to two decimal places.)


(ii) Find the p-value. (Round your answer to four decimal places.)


(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.

Answer 1

Given,

polish	A	B	C	D	E	Total
Frequency : Observed frequency	26	18	14	21	21	100

a) State the hypothesis for "no preference" in statistical terminology.

Ho: P(A) = P(B) = P(C) = P(D) = P(E) = 0.2

(b) What test statistic will be used in testing this null hypothesis?

(c) Complete the hypothesis test using α = 0.10.
(i) Find the test statistic. (Round your answer to two decimal places.)

Test Statistic

O : Observed Frequency

E : Expected frequency

polish	A	B	C	D	E	Total
Observed frequency:O	26	18	14	21	21	100
Expected Frequency: E	100*0.2=20	100*0.2=20	100*0.2=20	100*0.2=20	100*0.2=20	100

Test Statistic = 3.9

(ii) Find the p-value. (Round your answer to four decimal places.)
Degrees of freedom = Number of categories - 1= Number of polish types -1 =5-1=4

For 4 degrees of freedom,

p-value = 0.4197
(iii) State the appropriate conclusion.

Given level of significance =0.10;

As p-value : 0.4197 > level of significance :0.10; Do not reject Ho

Do not reject H0. There is no evidence of a consumer preference.