Test Hypotheses Regarding the Difference of Two Independent Means
-Find $\mu _ { 1 } \neq \mu _ { 2 }$

question 1

Multiple Choice

Test Hypotheses Regarding the Difference of Two Independent Means
-Find the standardized test statistic, t, to test the hypothesis that $\mu _ { 1 } \neq \mu _ { 2 }$ . Two samples are randomly selected and come from populations that are normal. The sample statistics are given below.
$$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } } 1 = 5.1 & \overline { \mathrm { x } } 2 = 5.5 \\\mathrm {~s} 1 = 0.76 & \mathrm {~s} _ { 2 } = 0.51\end{array}$$

• A) \(\mathbf { - 1 . 5 4 6 }\)
• B) \(- 1.821\)
• C) \(- 2.123\)
• D) \(- 1.326\)

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Definitions:

Short-Run Costs

Costs that vary depending on the level of production or output in the short term, where some factors of production are fixed.

Zero Economic Profits

A situation in which a firm's total revenues are exactly equal to its total costs, including opportunity costs, indicating neither an economic profit nor loss.

Long-Run Equilibrium

A market state where all producers and consumers have fully adjusted to all changes, and there are no forces causing further adjustments.

Production Costs

The total expense incurred in manufacturing a product or providing a service, including raw materials, labor, and overheads.