Construct a Confidence Interval For $\mu _ { d }$ , the Mean of the Differences

question 19

Multiple Choice

Construct a confidence interval for $\mu _ { d }$ , the mean of the differences $d$ for the population of paired data. Assume that the population of paired differences is normally distributed. A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a $99 \%$ confidence interval for the mean difference between the before and after scores.
$\begin{array}{llllllllllll}\text { Before }&70 & 80 & 92 & 99 & 93 & 97 & 76 & 63 & 68 & 71 & 74 \\\hline \text { After } & 69 & 79 & 90 & 96 & 91 & 95 & 75 & 64 & 62 & 64 & 76\end{array}$

• A) \(- 0.5 < \mu _ { d } < 4.5\)
• B) \(- 0.2 < \mu _ { d } < 4.2\)
• C) \(- 0.1 < \mu _ { d } < 4.1\)
• D) \(1.2 < \mu _ { d } < 2.8\)

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Definitions:

Marginal Cost

An additional cost incurred by producing one more unit of a product or service, a key concept in economics for decision-making.

Inverse Demand Curve

A graphical representation showing the relationship between the price of a good and the quantity demanded when price is the independent variable.

Cournot Duopolists

Firms in a duopoly market structure (two firms) where each firm determines its production level assuming the other firm's production level is fixed, as in the Cournot competition model.

Marginal Costs

The fluctuation in complete costs associated with an increase in production by a single unit.