Final answer:
The company should use an Analysis of Variance (ANOVA) test to compare the average heating bills for apartments in three different neighborhoods. If the p-value is below 0.05, it indicates a significant difference in at least one neighborhood's average heating bill.
Step-by-step explanation:
To determine whether there is a significant difference among the average heating bills for apartments in three different neighborhoods managed by Northwest Real Estate, a statistical test known as Analysis of Variance (ANOVA) should be used. This test is designed to compare the means of three or more samples to see if at least one of them significantly differs from the others. It is crucial to ensure that the assumptions for ANOVA are met, including the independence of samples, normal distribution of the populations, and equal variances among the groups.
Upon conducting the ANOVA, if the p-value is less than the significance level of 0.05, it can be concluded that there is at least one significant difference in the average heating bills among the different neighborhoods. Further post-hoc tests such as Tukey's HSD can help determine which specific groups' means are significantly different from each other.