In 2017, based on data for all homes in a certain city, the mean cost of residential electric bills was $279 per home. In 2019, based on a random sample of 12 homes, the cost of electric bills had a sample mean of $305.72 per home and the sample standard deviation of $40.05. In 2020, based on a random sample of 15 homes, the cost of electric bills had a sample mean of $326.45 per home and the sample standard deviation of $53.25. Use this information to answer parts (a) - (f). Assume that all the assumptions are met for the required analysis.

(a) Perform the most appropriate test to determine whether there was a difference in the mean cost of electric bills between 2017 and 2019. Test this at the 5% significance level.

(b) Find a 99% confidence interval for the mean cost of electric bills in 2019. Also, based on this confidence interval, state whether there is sufficient evidence to conclude that there was a difference in the mean cost of electric bills between 2017 and 2019 and explain the logic of your answer.

(c) Compare your answers in parts (a) and (b) and explain why these either gave you the same conclusion or different conclusions.

(d) Perform the most appropriate test to determine whether there was a difference in the mean cost of electric bills between 2019 and 2020. Test this at the 5% significance level.

(e) Find a 95% confidence interval for the difference in the mean cost of electric bills between 2019 and 2020. Also, based on this confidence interval, state whether there is sufficient evidence to conclude that there was a difference in the mean cost of electric bills between 2019 and 2020 and explain the logic of your answer.

(f) Compare your answers in parts (d) and (e) and give two reasons why these either gave you the same conclusion or different conclusions