Three supermarket chains in the Denver area each claims to have the lowest overa

Question

Three supermarket chains in the Denver area each claims to have the lowest overall prices. As part of an investigative study on supermarket advertising, the Denver Daily News conducted a study. First, a random sample of nine grocery items was selected. Next, the price of each selected item was checked at each of the three chains on the same day. At the 0.025 significance level, is there a difference in the mean prices at the supermarkets or for the items? Item Super$ Ralph's Lowblaws 1 $1.29 $4.36 $3.10 2 1.37 1.87 1.87 3 1.21 2.40 1.72 4 2.01 4.15 2.22 5 1.57 2.10 2.40 6 1.35 5.05 4.21 7 2.46 3.75 3.90 8 1.25 3.10 4.21 9 2.40 4.15 1.80

Explanation / Answer

(d) The p- value is 0.977 Since this is >0.025

we fail to reject H0

.

Item Super$ Ralphs Lowblaws 1 1.29 4.36 3.10 2 1.37 1.87 1.87 3 1.21 2.40 1.72 4 2.01 4.15 2.22 5 1.57 2.10 2.40 6 1.35 5.05 4.21 7 2.46 3.75 3.90 8 2.25 3.10 4.21 9 2.40 4.15 1.80 (a) H0: There is no difference between the mean prices at the three stores; that is, m1 = m2 = m3 Ha: At least in one store, the price is different from the other two; that is, at least one of m1, m2 and m3 is different from the other two. (b) One-way ANOVA with a=0.025 Decision Rule: Reject H0 if the p- value <0.025

(d) The p- value is 0.977 Since this is >0.025

we fail to reject H0

.

(e) Conclusion: There is no sufficient evidence that the mean prices are different. Anova: Single Factor SUMMARY Groups Count Sum Average Variance Super$ 9 15.9 1.767777778 3.230169444 Ralphs 9 30.93 3.436666667 1.250049997 Lowblaws 9 25.43 2.825555556 1.099752775 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.13702963 2 0.068514815 0.022848836 0.98902 3.402826105 Within Groups 71.96671111 24 2.998612963 Total 74.55278173 26

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