A home builder claims that the addition of a heat pump will

A home builder claims that the addition of a heat pump will reduce electric bills in all-electric homes. To support this claim he obtains the electricity bills for 7 customers for the month of January for two consecutive years, one before the heat pump was installed and one after.

Which statistical test is appropriate to determine if there is sufficient evidence to show that heating bills were reduced?

Solution

Before stating any test we will have to assume that the electricity cost and the amount of power consumed remains same in both the years.

Given the assumptions satisfied, we can use a one tailed, paired sample t-test for the mean difference betwween the bill amounts.

Consider the first sample to be that without heat pump and the second sample to be the one after installing the heat pump. As both sample data are collected from the same set of 7 customers, so the data of the two sample s are paired. And as we need to test whether the bill has reduced, so it is a one-tailed test.