Oneway

ANOVA
Household Grocery Order Amounts $ Sum of Squares df Mean Square F Sig.
Between Groups 29343.557 2 14671.778 7.128 .001
Within Groups 177019.882 86 2058.371
Total 206363.438 88

Post Hoc Test
Multiple Comparisons
Household Grocery Order Amounts $
Tukey HSD
(I) Cities (J) Cities Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound
St. Catherines Edmonton -42.50460* 11.81485 .002 -70.6825 -14.3266 Moncton -9.23333 11.71430 .711 -37.1715 18.7048
Edmonton St. Catherines 42.50460* 11.81485 .002 14.3266 70.6825 Moncton 33.27126* 11.81485 .016 5.0933 61.4492
Moncton St. Catherines 9.23333 11.71430 .711 -18.7048 37.1715 Edmonton -33.27126* 11.81485 .016 -61.4492 -5.0933
*. The mean difference is significant at the 0.05 level.

Homogeneous Subsets
Household Grocery Order Amounts $
Tukey HSDa,b
Cities N Subset for alpha = 0.05 1 2
St. Catherines 30 93.6333
Moncton 30 102.8667
Edmonton 29 136.1379
Sig. .714 1.000
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 29.659.
b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

Question # 3

Is there a significant difference in the mean household grocery order amounts in St. Catherines, Edmonton and Moncton. If there is a difference among the means, indicate where orders are higher and/or lower.

To determine whether there is a difference among the means of each city, a one-way ANOVA test will be performed. A level of significance of 0.05 will be used. We will assume that the populations are normally distributed, the populations have equal variances and the samples are randomly and independently drawn.

Hypothesis:

µ1 = household grocery order amounts from St. Catherines µ2 = household grocery order amounts from Edmonton µ3 = household grocery order amounts from Moncton α = 0.05 level of significance
Ho: µ1 = µ2 = µ3
Ha: Not all of the population means are the same
- at least one μj is different; j = 1, 2, 3

Results:

F Critical Value = 3.103
Fcalc = 7.128 p-value = 0.001
∴ p-value < α

With a p-value of 0.001 and a 0.05 level of significance, we reject the null hypothesis because the p-value is less than the specified level of significance. Therefore, there is evidence that at least one μj differs from the rest.

Mean Grocery Order Amounts from St. Catherines to Edmonton:
Ho: µ1 = µ2
Ha: µ1 ≠ µ2 p-value = 0.002

Since the p-value = 0.002 < 0.05, the conclusion is to reject the null hypothesis and there is evidence to indicate that the means for St. Catherines and Edmonton are different. There is also evidence to indicate that the household grocery order amounts are higher in Edmonton because of the negative mean difference between the two cities.

Mean Grocery Order Amounts from St. Catherines to Moncton:
Ho: µ1 = µ3
Ha: µ1 ≠ µ3 p-value = 0.711
Since the p-value = 0.711 > 0.05, the conclusion is to not reject the null hypothesis and there is no evidence to indicate that the means for St. Catherines to Moncton are different. There is also evidence to indicate that the household grocery order amounts are higher in Moncton because of the negative mean difference between the two cities.

Mean Grocery Order Amounts from Edmonton to Moncton:
Ho: µ2 = µ3
Ha: µ2 ≠ µ3 p-value = 0.016

Since the p-value = 0.016 < 0.05, the conclusion is to reject the null hypothesis and there is evidence to indicate that the means for Edmonton to Moncton are different. There is also evidence to indicate that the household grocery order amounts are higher in Edmonton because of the positive mean difference between the two cities.

Therefore, through the use of multiple comparisons, it is evident that Edmonton has the highest mean household grocery order amounts and St. Catherines has the lowest mean household grocery order amounts.