Question

1. A business consultant believes consumers equally prefer four brands of coffee (A, B, C, D). He collects a random sample of 400 consumers with the following results on preferences:

   Observed

   Frequency

Brand              of Preferences

               A                          102

               B                          121

               C                          120

               D                            57

Use a Excel spreadsheet to test this hypothesis at the 0.05 level. Submit the Excel spreadsheet you create along with an explanation of results (either in your pdf or on the Excel spreadsheet).

Answer 1

let P1,P2,P3,P4 denotes the proportion of peoples prefer brands A,B,C and D respectively

so we need to test that

H0:P1=P2=P3=P4=0.25

H1: proportions are different

now calculating expected frequencies under H0 and the calculating chi-square statistics

Expected Frequency =N*P

Chi square statistics given by

now using excel we have calculated that

Brand	Observed	Expected=n*Pi=400*Pi	U=(Observed-expected)^2	U/expected
A	102	100	4	0.039216
B	121	100	441	3.644628
C	120	100	400	3.333333
D	57	100	1849	32.4386
Total				39.45577

CHi square value =39.46

Chi Square DF=n-1=4-1=3

Now P value =P(chi square >39.46) <0.00001

Since PValue is very less than level of significance hence we reject H0 hence there is enough evidence to conclude that proportions of prefereing brands A,B,C and D are different.