Construct a 95\% confidence interval for the predicted mean total cholesterol of all 42-year-old females using the data in Table 1.

Approach Determine a confidence interval for the predicted mean total cholesterol at \(x^{*}=42\) using Formula (1), since our estimate is for the mean cholesterol of all 42-year-old females.

Formula 1

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Table 1 Age,x Total Cholesterol, y Age,.x Total Cholesterol, y 25 180 42 183 25 195 48 204 28 186 51 221 32 180 51 243 32 210 58 208 32 197 62 228 38 239 65 269