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

question 27

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


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

$\begin{array}{lrrrr} & \text { PARAMETER } & \text { STANDARD } & \text { T FOR 0: } & \\\text { VARIABLE } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB > }|\mathrm{T}| \\\text { INTERCEPT } & 11.98 & 80.50 & 0.15 & 0.885 \\\text { X1(TEST1) } & 0.2745 & 0.1111 & 2.47 & 0.039 \\\text { X2(TEST2) } & 0.3762 & 0.0986 & 3.82 & 0.005 \\\text { X3(TEST3) } & 0.3265 & 0.0808 & 4.04 & 0.004\end{array}$

Suppose the $95 \%$ confidence interval for $\beta _ { 3 }$ is $( .15 , .47 )$ . Which of the following statements is incorrect?

• A) We are \(95 \%\) confident that the Test 3 is a useful linear predictor of Test 4 score, holding Test1 and Test2 fixed.
• B) At \(\alpha = .05\), there is insufficient evidence to reject \(H _ { 0 } : \beta _ { 3 } = 0\) in favor of \(H _ { \mathrm { a } } : \beta 3 \neq 0\).
• C) We are \(95 \%\) confident that the increase in Test4 score for every 1-point increase in Test3 score falls between \(.15\) and \(.47\), holding Test1 and Test 2 fixed.
• D) We are \(95 \%\) confident that the estimated slope for the Test4-Test3 line falls between \(.15\) and \(.47\) holding Test1 and Test2 fixed.

Calculate the impact of fees on mutual fund investments and understand the concept of load and no-load funds.

Recognize the benefits of mutual funds in retirement accounts and the ability to switch investments in a family of funds concept.

Understand the categories of corporate social responsibility (CSR) approaches and be able to identify them in real business scenarios.

Grasp the concept of sustainability and its application within the finance and corporate sectors for the betterment of future generations.

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Definitions:

Protein

Organic molecules made up of amino acids that are essential for many processes in living organisms, including catalysis of metabolic reactions and DNA replication.

Generalization

The process of formulating general concepts by abstracting common properties of specific instances, thus allowing for broader applications or interpretations.

Businesses

Organizations engaged in commercial, industrial, or professional activities aimed at generating profits.

Building

A structure with a roof and walls, such as a house, school, or factory, used for shelter, work, or storage.