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	28	17	16	23	16	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) = 0.2     H₀: P(x) = P(y) for some x and y H₀: P(A) + P(B) + P(C) + P(D) + P(E) = 1

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

p χ²     z t μ

(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.

Answer 1

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

b)

χ²

c)

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.200	28.000	20.00	1.79	3.200
2	0.200	17.000	20.00	-0.67	0.450
2	0.200	16.000	20.00	-0.89	0.800
2	0.200	23.000	20.00	0.67	0.450
3	0.200	16.000	20.00	-0.89	0.800
total	1.000	100	100		5.700

test statistic =5.700

ii)

_0.2_< p <_0.3

iii)

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