Construct the Indicated Confidence Interval for the Difference Between the Two

question 24

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Independent samples from two different populations yield the following data.
$\bar { x } _ { 1 } = 958 , \bar { x } _ { 2 } = 157 , s _ { 1 } = 77 , s _ { 2 } = 88$
The sample size is 478 for both samples. Find the 85% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$

• A) \(781 < \mu _ { 1 } - \mu _ { 2 } < 821\)
• B) \(800 < \mu _ { 1 } - \mu _ { 2 } < 802\)
• C) \(794 < \mu _ { 1 } - \mu _ { 2 } < 808\)
• D) \(791 < \mu _ { 1 } - \mu _ { 2 } < 811\)

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Definitions:

Peak Efficiency

The optimal point at which a particular process or system operates with maximum effectiveness or efficiency.

MC = MR

The point where Marginal Cost equals Marginal Revenue, considered the optimal point of production for maximum profit.

ATC Curve

A graph showing the average total cost of production at different levels of output, illustrating how costs vary with changes in output.

Economic Profit

The difference between a firm's total revenues and its total costs, including both explicit and implicit costs, reflecting the total financial gain.