A Study Contains a Plot of the Following Data Pairs

question 53

Essay

A study contains a plot of the following data pairs, where x = pressure of extracted gas (microns) and y = extraction time (min): $$\begin{array} { l l l l l l l l l l l } \hline x & 40 & 130 & 155 & 160 & 260 & 275 & 325 & 370 & 420 & 480 \\\hline y & 2.5 & 3.0 & 3.1 & 3.3 & 3.7 & 4.1 & 4.3 & 4.8 & 5.0 & 5.4 \\\hline\end{array}$$
a. Estimate $\sigma$
and the standard deviation of $\hat { \beta } _ { 1 }$
b. Suppose the investigators had believed prior to the experiment that on average there would be an increase of .006 min. in extraction time associated with an increase of 1 micron in pressure. Use the P-value approach with a significance level of .10 to decide whether the data contradicts this prior belief.

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Definitions:

Operating Income

Earnings before interest and taxes (EBIT), calculated as gross income minus operating expenses, excluding non-operating income and expenses.

Variable Product Cost

Costs that vary directly with the level of production, such as materials and labor.

Total Fixed Overhead

The sum of all costs that remain constant regardless of the level of production or sales, such as rent, salaries, and insurance.

Contribution Margin

The amount remaining from sales revenue after variable costs have been deducted, used to cover fixed costs and to generate profit.