Problem 2. aside from the excise tax on purchase sugar-sweetened beverages, another provision of the tax reform program is the excise tax on fuel and automobiles. the higher tax aims to discourage too much consumption of scarce resources and to control environmental pollution. the economic team assessed the current consumption of fuel among students who drive to school as baseline for possible changes in the students’ fuel consumption after one year. the team randomly selected 10 students who drive to school and asked the amount they spend on fuel per month. the following expenses were given: 5,500 4,600 6,000 8,000 1,000 6,700 2,200 7,000 3,500 2,500 it is known that monthly expenses on fuel follow the normal distribution with standard deviation of 500 pesos.
a. construct a 95% confidence interval for the true mean monthly expenditure on fuel. interpret the confidence interval obtained. (6 pts)
b. find a 99% confidence interval for the true mean monthly expenditure on fuel (3 pts)
c. calculate the widths of the confidence intervals in (a) and (b). how was the width of the confidence interval affected by the decrease in the level of confidence? (4pts)