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) \(1.2 < \mu _ { d } < 2.8\)

---

Definitions:

Demand Function

A mathematical expression that shows the relationship between the quantity of a good that consumers are willing and able to purchase and its price, along with other determinants of demand.

Profit-Maximizing

The process or strategy by which a firm determines the price and output level that returns the greatest profit.

Monopolist

A market participant that is the sole provider of a good or service, giving them significant control over pricing and market conditions.

Variable Costs

Expenses that change in proportion to the activity of a business.