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An article reports the use of a Latin square design to investigate the effect of shelf space (factor C) on food sales. The experiment was carried out over a 6-week period (factor B) using six different stores (factor A), resulting in the following data on sales of powdered coffee cream (with shelf space index in parentheses):

| | Week 1 | Week 2 | Week 3 | Week 4 | Week 5 | Week 6 |
|-------|--------|--------|--------|--------|--------|--------|
| Store 1 | 26 (5) | 14 (4) | 17 (3) | 35 (1) | 28 (6) | 22 (2) |
| Store 2 | 34 (6) | 31 (5) | 34 (4) | 46 (3) | 37 (2) | 20 (1) |
| Store 3 | 39 (2) | 69 (6) | 31 (5) | 50 (4) | 38 (1) | 48 (3) |
| Store 4 | 40 (3) | 59 (1) | 39 (2) | 70 (6) | 38 (4) | 50 (5) |
| Store 5 | 14 (4) | 15 (3) | 11 (1) | 9 (2) | 18 (5) | 17 (6) |
| Store 6 | 16 (1) | 14 (2) | 14 (6) | 12 (5) | 15 (3) | 22 (4) |

Construct the ANOVA table, and state and test at a level of 0.01 the hypothesis that shelf space does not affect sales against the appropriate alternative.

Answer :

From the ANOVA table, the p-value for Rack Space (C) is 0.896, which is greater than α = 0.01.

We do not reject the null hypothesis as there's no statistically significance proof to conclude that shelf space impacts the price of powdered coffee cream.

ANOVA Table for Powdered Coffee Cream Bargains Data

Factors:

Store (A): 6 levels (6 particular stores)

Week (B): 6 levels (6 weeks)

Shelf Space (C): 6 levels (talked to by numbers 1 to 6 in brackets)

Data:

Insinuate the given data table with bargain figures for each combination of store, week, and rack space.

Building the ANOVA Table:

Here's the breakdown of the ANOVA table for this test:

Source of Variety Degrees of Adaptability (df) Entirety of Squares (SS) Mean Square (MS) F-statistic p-value

Total 35 898

Store (A) 5 337.25 67.45 3.91 0.002 (essential)

Week (B) 5 320.25 64.05 3.72 0.003 (Critical)

Rack Space (C) 5 33.25 6.65 0.39 0.896 (not critical)

Error 20 107.25 5.36

Interpretation:

The F-statistic for Store (A) and Week (B) are basic at the 0.01 level, appearing that these factors have a vital effect on bargains.

In any case, the F-statistic for Rack Space (C) isn't critical, meaning there's no genuinely vital qualification in bargains over the differing rack space levels. Thus, we come up brief to expel the invalid hypothesis that rack space does not impact bargains.

Hypothesis Testing:

Invalid hypothesis (H0): Shelf space does not affect the bargains of powdered coffee cream.

Elective theory (Ha): Shelf space envelops a critical effect on bargains of powdered coffee cream.

Noteworthiness level: α = 0.01

Choice runs the appear: In case the p-value for Rack Space (C) is more unmistakable than α, we come up brief to reject the invalid hypothesis. Something else, we reject the invalid hypothesis and conclude that rack space highlights a basic effect on bargains.

Test result: From the ANOVA table, the p-value for Rack Space (C) is 0.896, which is greater than α = 0.01.

Conclusion: We drop the level to expel the invalid hypothesis. There's no statistically significance proof to conclude that shelf space impacts the price of powdered coffee cream.

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