QUESTION 2 I. A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond \( y \) is thought to be a linear function of the age of the propellant \( x \) when the motor is cast. Ten observations are shown in the table: \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Strength ' \( y \) ' (psi) & 2159 & \( 1678.2 \) & 2316 & 2061 & 2208 & 1708 & 1785 & 2575 & 2358 & 2278 \\ \hline Age ' \( x \) ' (weeks) & \( 15.5 \) & \( 23.75 \) & 8 & 17 & 5 & 19 & 24 & \( 2.5 \) & \( 7.5 \) & 11 \\ \hline \end{tabular} (a) Investigate the simple linear regression model by using least squares' estimates of the slope and intercept. (b) Figure out the mean shear strength of a motor made from propellant that is 20 weeks old. (c) Analyze the correlation by using Karl Pearson's coefficient.
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The shear strength of the bond between two propellants is important in rocket engines. The following table shows the age of the propellant $t$ (in days) and the shear strength $s$ (in psi). Find the equation of the regression line and then estimate the shear strength for propellant that is 7 days old. Is this interpolation or extrapolation? $$\begin{array}{l|r|r|r|r|r|r}\text {Age of propellant}, & & & & & \\t \text { (days) } & 14 & 56 & 88 & 133 & 150 & 167 \\\hline \text {Shear strength} \text { , } & & & & & & \\s \text { (psi) } & 2654 & 2316 & 2200 & 1708 & 1754 & 1678\end{array}$$
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