During Its Manufacture, a Product Is Subjected to Four Different $( y )$

question 17

Multiple Choice

During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score $( y )$ , as a function of Test1 score $\left( x _ { 1 } \right)$ ) , Test 2 score $\left( x _ { 2 } \right)$ , and Test3 score $\left( x _ { 3 } \right)$ . [Note: All test scores range from 200 to 800 , with higher scores indicative of a higher quality product.] Consider the model:
$$E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }$$
The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout.

$\begin{array}{lrrrrr}\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { FVALUE } & \text { PROB > F } \\\text { MODEL } & 3 & 151417 & 50472 & 18.16 & .0075 \\\text { ERROR } & 8 & 22231 & 2779 & & \\\text { TOTAL } & 12 & 173648 & & &\end{array}$

$\begin{array}{llll}\text { ROOT MSE } & 52.72 & \text { R-SQUARE } & 0.872 \\\text { DEP MEAN } & 645.8 & \text { ADJ R-SQ } & 0.824\end{array}$

$\begin{array} { l l l l } & \text {PARAMETER }& \text {STANDARD}& \text {T FOR 0:}\\ \text {VARIABLES}&\text { ESTIMATE } & \text { ERROR } & \text { PARAMETER } = 0 & \text { PROB } > | T | \end{array}$


$\begin{array} { l r r r r } \text { INTERCEPT } & 11.98 & 80.50 & 0.15 & 0.885 \\\text { X1(TEST1) } & 0.2745 & 0.1111 & 2.47 & 0.039 \\\text { X2(TEST2) } & 0.3762 & 0.0986 & 3.82 & 0.005 \\\text { X3(TEST3) } & 0.3265 & 0.0808 & 4.04 & 0.004 \\\hline\end{array}$




Compute a $95 \%$ confidence interval for $\beta _ { 3 }$ .

• A) \(.33 \pm 105\)
• B) \(.33 \pm 4.04\)
• C) \(.33 \pm .08\)
• D) \(.33 \pm .19\)

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Definitions:

Defined Benefit Pension Plan

A retirement plan where employer commitments are based on a formula considering factors like salary history and duration of employment, with the company bearing investment risk.

Prior Service Cost Amortization

The process of expensing the costs of retroactive benefits granted in a pension plan over a period of time.

Actuarially Determined Discount Rate

This refers to the interest rate used in the actuarial valuation to discount future pension obligations to present value, reflecting the expected rate at which the pension plan's liabilities can be funded or settled.

Pension Liability

The amount of money a company is required to pay into its employees' retirement plans in the future.