Problem 3 [15 points = 10 + 5] A study of the population average change in property tax was conducted by a County Clerk Office. With this purpose, they randomly selected n = 16 households and collected paired records (X, Y) about their property tax for two consecutive years. Here X is the amount of property tax paid for the previous year and Y is the tax assessment for this year. Individual differences, D = Y - X are 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, a = 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 with C = 95% confidence. Solution