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6.

Data given below are on the adjusted gross income :0 and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation :9 = 4.68 + 0.169;, the point estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52,500 is $13,080. Click on the datafile to reference the data. Excel File: data 1437.x|sx Adjusted Gross Reasonable Amount of Itemized Income ($10005) Deductions ($1000s) 22 9.6 27 9.6 32 10.1 48 1 1.1 65 13.5 85 17.7 120 25.5 Use the estimated regression coefficients rounded to 2 decimals in your calculations. a. Develop a 95% confidence interval for the mean amount of total itemized deductions for all taxpayers with an adjusted gross income of $52,500 (to 2 decimals). $ 11647. ethousand to$ 14512. ethousand b. Develop a 95% prediction interval estimate for the amount of total itemized deductions for a particular taxpayer with an adjusted gross income of $52,500 (to 2 decimals). $ 9273.9 0 thousand to $ 16886. 0 thousand c. If the particular taxpayer referred to in part (b) claimed total itemized deductions of $20,400, would the IRS agent's request for an audit appear to be justified? Ya. v M, it is w than anticipated. d. Use your answer to part (b) to give the IRS agent a guideline as to the amount of total itemized deductions a taxpayer with an adjusted gross income of $52,500 should claim before an audit is recommended (to the nearest whole number). Any deductions exceeding the $ 20400 0 upper limit could suggest an audit. \fJensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage Annual (hours) Maintenance Expense 20 24 17 29 27 37 35 44 39 54 24 38 31 40 38 46 47 59 45 47 a. Develop the estimated regression equation that relates annual maintenance expense (in hundreds of dollars) to weekly usage hours (to 3 decimals). A Expense = 10.917 Q9 + 0.956 Q0 Weekly Usage b. Test the significance of the relationship in part (a) at a 0.05 level of significance. Compute the value of the F test statistic (to 2 decimals). 45.92 Q0 Thevapnueisw What is your conclusion? ' Conclude that there is a significant relationship between expense and weekly usage V, w c. Jensen expects the new machine to be used 30 hours per week. What is the expected annual maintenance expense in hundreds of dollars (to 2 decimals)? $ 0 hundred Develop a 95% prediction interval for the company's annual maintenance expense for this machine (to 2 decimals). ($ 0 hundred, $ 0 hundred)