# One-Way Anova Problem - Bottle Design

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A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid laundry detergent was carried out using a randomized block experimental design, with supermarkets as blocks. Specifically, four supermarkets were supplied with all three-bottle designs, which were priced the same. The table below gives the number of bottles of each design sold in a 24-hour period at each supermarket. If we use these data, SST, SSB, and SSE can be calculated to be 586.1667, 421.6667, and 1.8333, respectively.

a Test the null hypothesis H0 that no differences exist between the effects of the bottle design on mean daily sales. Set a _ .05. Can we conclude that the different bottle designs have different effects on mean sales?

b Test the null hypothesis H0 that no differences exist between the effects of the supermarkets on mean daily sales. Set a _ .05. Can we conclude that the different supermarkets have different effects on mean sales?

c Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the bottle design effects on mean daily sales. Which bottle design(s) maximize mean sales?

Results of a Bottle Design Experiment

Supermarket, j

Bottle Design, I 1 2 3 4

A 16 14 1 6

B 33 30 19 23

C 23 21 8 12

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##### Solution Summary

The solution contains detailed explanation of testing hypotheses using the five-step procedures.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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