A study of the population average change in property tax was conducted by a County Clerk Office. With this purpose, they randomly selectedn= 16 households and collected paired records (X, Y) about their property tax for two consecutive years. HereXis the amount of property tax paid for the previous year andYis the tax assessment for this year. Individual differences,D=Y Xare assumed to be normally distributed with unknown parameters.

Sample summaries are shown below.

_{(Year 2020) =X= $4,698 and (Year 2021) =Y}= $3,456

while the sample standard deviation based on individual differences was

SD =S= $2,000

1. At the significance level,= 0.01,do you have sufficient evidence to conclude that the population average property tax has decreased from years 2020 to year 2021?

Evaluate the Test Statistic

Specify the Critical Value and state Rejection Rule

2. Estimate the population average change in property tax withC= 95% confidence.