With reference to Exercise 11.16, find a \(90 \%\) confidence interval for \(\alpha\).

Data From Exercise 11.16

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11.16 Recycling concrete aggregate is an important compo- nent of green engineering. The strength of any po- tential material, expressed in terms of its resilient modulus, must meet standards before it is incorpo- rated in the base of new roadways. There are two methods of obtaining the resilient modulus. The ex- terior measurement Mext (MPa) and interior mea- surement Mint (MPa) can be measured on each sam- ple. The results for n = 9 samples are (Courtesy of Tuncer Edil) Mext| 204.7 184.8 181.1 166.5 165.2 154.1 135.8 173.4 142.7 M; int 707.1 632.2 603.6 522.4 554.4 483.5 449.7 545.1 473.8 (a) Draw a scatter plot to verify the assumption that the relationship is linear, letting Mint be x and Mext be y. (b) Fit a straight line to these data by the method of least squares, and draw its graph on the diagram obtained in part (a).