Find the Critical Value $t _ { 0 }$ To Test the Claim That

question 23

Multiple Choice

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.02$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } } 1 = 3.9 & \overline { \mathrm { x } _ { 2 } } = 4.3 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51\end{array}$$

• A) \(\pm 2.764\)
• B) \(\pm 0.684\)
• C) \(\pm 2.228\)
• D) \(\pm 3.169\)

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Definitions:

Diminishing Returns

A principle stating that if one factor of production is increased while others are held constant, the output per unit of the variable factor will eventually decrease.

ATC

An abbreviation for Average Total Cost, a financial metric calculated by dividing the total cost by the quantity of output produced.

MC

Often referred to as Marginal Cost, it is the increase in total cost that arises from an extra unit of production.

Inputs

Resources used in the production process to produce goods or services.