Construct a Confidence Interval for µD, the Mean of the Differences

question 16

Multiple Choice

Construct a confidence interval for µd, 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.
$\begin{array} { l l l l l l l l l l l l } \text{Before} & 70 & 80 & 92 & 99 & 93 & 97 & 76 & 63 & 68 & 71 & 74 \\ \hline \text{After} & 69 & 79 & 90 & 96 & 91 & 95 & 75 & 64 & 62 & 64 & 76 \end{array}$

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

---

Definitions:

Rational Expectations School

An economic idea that assumes individuals make predictions about the future based on all available information and past experiences in a rational manner.

Monetary Policy

The process by which a central bank controls the supply of money in an economy, typically targeting inflation, employment, and economic growth.

Potential Level

The potential level of output, or potential GDP, is the maximum amount of goods and services an economy can produce when it is fully utilizing its resources, without causing inflation to rise.

Fixed-growth-rate Monetary Policy

A monetary policy framework aiming to maintain a predetermined rate of growth in the money supply.