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

question 56

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

• A) \(- 0.5 < \mu _ { d } < 4.5\)
• 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:

Operational Definition

A clear, precise description of a variable in terms of the operations or techniques used to measure or manipulate it in a research study.

Variable

A characteristic, number, or quantity that increases or decreases over time, or takes different values in different situations.

Behavior Pattern

Repeated, often unconscious ways of acting or responding that become characteristic of a person over time.

Independent Variable

In experimental settings, the variable that is manipulated or changed to observe its effect on the dependent variable.