Question

Several types of yogurt are sold in a small general store. From a past study of customer​ selections, the owner knows that 25​% of the customers ordered flavor​ A, 30​%, flavor​ B, 18​%, flavor​ C, 13​%, flavor​ D, and the​ remainder, flavor E. Now the​ owner, who thinks that the customer preferences have​ changed, randomly samples 80 customers and finds that 15 prefer​ A, 17 prefer​ B, 30 prefer​ C, 7 7 prefer E and the remainder prefer D. Determine if the​ customers' preferences have changed from the last study. Use significance level alpha α equals = 0.05

Answer 1

null hypothesis: Ho: ​ customers' preferences is same as from the last study.

alternate hypothesis:Ha: ​ customers' preferences have changed from the last study.

degree of freedom =categories-1=

4

for 0.05 level and 4 degree of freedom :rejection region =

9.488

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.250	15	20.000	-1.12	1.250
B	0.300	17	24.000	-1.43	2.042
C	0.180	30	14.400	4.11	16.900
D	0.130	11	10.400	0.19	0.035
E	0.140	7	11.200	-1.25	1.575
total	1.000	80	80		21.801

as test statistic 21.801 is in rejection region ; we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that customers' preferences have changed from the last study.