Question

4. A private-label bottler of soft drinks asks each of 60 members of a tasting panel (who are regarded as a random sample from millions of potential customers) to rate each of two possible formulations of a cola drink on a 100-point scale; higher scores are desirable. Formulation G is less expensive and will be used unless there is a clear evidence that formulation R is preferred. From the data, the bottler obtains the difference (R-G) in the ratings for each panelist. After conducting appropriate statistical tests on the mean of the differences in the ratings, the management of the private-label bottler concluded that the difference in the ratings is negligible. Consequently, they have decided to use formulation G which is less expensive. The data on the panelist’s ratings they have used is in the Excel data file named ‘Cola Ratings’. Using the same data and at 10% level of significance, please conduct the test you think the management’s decision must have been based on. Based on your results, do you agree with the management’s conclusion? Does your conclusion change at 5% level of significance?

G	R
57	62
46	58
85	81
80	88
95	84
31	54
56	44
40	65
52	37
26	51
93	76
54	43
67	64
42	59
29	51
81	70
35	49
59	61
44	57
84	97
34	55
49	44
73	86
74	89
44	52
41	49
72	61
60	48
48	69
92	87
64	77
52	47
58	66
84	80
60	50
49	38
96	74
20	49
42	19
36	58
69	48
44	56
37	59
57	29
31	62
74	51
85	79
19	52
33	76
48	80
88	84
72	64
45	58
36	42
64	85
77	75
28	22
93	87
45	48
50	40

Answer 1

G		R
Mean	56.65	Mean	60.76666667
Standard Error	2.702146562	Standard Error	2.26348647
Median	53	Median	58.5
Mode	44	Mode	58
Standard Deviation	20.93073727	Standard Deviation	17.5328908
Sample Variance	438.0957627	Sample Variance	307.4022599
Kurtosis	-0.937467288	Kurtosis	-0.436751072
Skewness	0.264852348	Skewness	-0.033675571
Range	77	Range	78
Minimum	19	Minimum	19
Maximum	96	Maximum	97
Sum	3399	Sum	3646
Count	60	Count	60

Based on your results, we agree with the management’s conclusion.

Does your conclusion change at 5% level of significance?

For a 5% level of significance.