Question

A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table Bottle Design Study Data 35 35 30 26 20 25 21 26 16 19 16 18 16 You will need to enter the data into Minitab. It is easiest to copy from here into Excel. Then copy and paste from Excel into Minitab. Besure that row 1 (the first white row in the spreadsheet) contains the first piece of data and that variable names are in the top grey row in Minitab. (a) Test the null hypothesis that c are equal by setting a ะ 05 Based on this test, can we A.WB, and conclude that bottle designs A, B, and C have different effects on mean daily sales? (Round your answers to 2 decimal places. Leave no cells blank - be certain to enter "O" wherever required.) p-value (Click to select) Ho bottle design (Click to select) have an impact on sales (b) Based on Tukey's results, which bottle design maximizes mean daily sales? Bottle design (Click to selecth) maximizes sales

Answer 1

a) We will set up null hypothesis

$H_{0}$ : $\mu$A = $\mu$​​​​​​​B = $\mu$C or All mean all equal

$H_{1}​​​​​​​$ : $\mu$A $\neq$$\mu$​​​​​​​B $\neq$ $\mu$C or All mean all not equal

The ANOVA table is given Below, results from Minitab

Source	DF	SS	MS	F	P
Factor	2	663.6	331.8	68.65	0.0000
Error	12	58	4.83
Total	14	721.6

F = 68.65

P-Value = 0.0000

We will reject H₀ as calculated P-Value = 0.0000 which is less then 0.05 and concludes that bottle design have significant impact on sales.

b)   
MSE

4.83 To.05(3,15-3)

  
4.83 T- 3.773

T-3.7083

now mean absolute difference

|$\mu$A - $\mu$​​​​​​​B|	16.2	>3.70	Difference is significant between between A and B
|$\mu$​​​​​​​A - $\mu$​​​​​​​C|	6.6	>3.70	Difference is significant between between A and C
|$\mu$​​​​​​​B - $\mu$​​​​​​​C|	9.6	>3.70	Difference is significant between between B and C