Construct a Confidence Interval for µD the Mean of the Differences

question 61

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. $\begin{array}{llllllllllll}\text { Before } & 70 & 80 & 92 & 99 & 93 & 97 & 76 & 63 & 68 & 71 & 74 \\\hline \text { After } & 69 & 79 & 90 & 96 & 91 & 95 & 75 & 64 & 62 & 64 & 76\end{array}$

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

---

Definitions:

Compounded Annually

Interest calculation method where interest is added to the principal once a year, leading to an exponential increase.

Compounded Semiannually

The process of calculating interest on both the initial principal and the accumulated interest from previous periods, done twice a year.

Monthly Compounding

The process of computing interest on an amount where the calculated interest is added to the principal at the end of each month for the purpose of calculating future interest.

Nominal Rate

The stated interest rate of an investment or loan, without taking into account inflation or compounding of interest.