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In the earlier exercise, data were given on the adjusted gross income xx and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation y^=4.68+.16x\hat{y}= 4.68 + .16x, the point estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of 52,500 dollars is 13,080 dollars. \newline Develop a 95%95\% confidence interval for the mean amount of total itemized deductions for all taxpayers with an adjusted gross income of 52,500 dollar.

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The mentioned exercise gives n=7n=7 data points, which are fitted to a linear model. This exercise focuses on point yy^* at x=52.5x^*=52.5. The formula for the (1α)100%(1-\alpha)\cdot 100\% confidence interval for E(y)E(y^*) is:

y^±tα/2sy^.\hat{y^*}\pm t_{\alpha/2}\cdot s_{\hat{y^*}}.

Estimation y^=13.08\hat{y^*}=13.08 from the regression equation is given.

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