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:

Equal Interest

A situation where all parties or stakeholders hold an identical percentage or stake in an agreement, asset, or entity, ensuring a fair distribution of rights and obligations.

Unanimous Consent

Unanimous consent refers to an agreement or decision made with the approval of all parties involved, often used in corporate governance contexts to expedite decisions without a formal vote.

AASB 11

An Australian accounting standard that addresses the accounting for interests in joint arrangements, specifying how an entity should report its interests.

Joint Arrangement

A contractual arrangement in which the parties involved have joint control over the decision making in relation to the joint arrangement.