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

question 8

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 abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. $\begin{array}{llllllllllll}\text { Before } & 74 & 83 & 75 & 88 & 84 & 63 & 93 & 84 & 91 & 77 \\\hline \text { After } & 73 & 77 & 70 & 77 & 74 & 67 & 95 & 83 & 84 & 75\end{array}$

• A) \(1.0 < \mu _ { \mathrm { d } } < 6.4\)
• B) \(0.2 < \mu _ { \mathrm { d } } < 7.2\)
• C) \(1.2 < \mu _ { \mathrm { d } } < 5.7\)
• D) \(0.8 < \mu _ { \mathrm { d } } < 6.6\)

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Definitions:

Dependent-Samples T Test

A statistical procedure used to compare the means of two related groups to find out if there is a significant difference between them.

Repeated Measures

Refers to experiments or tests in which the same subjects are tested under multiple conditions or at multiple time points.

Dependent-Samples T Test

A statistical test used to compare the means of two related groups or conditions to determine if there are statistically significant differences between them.

Average Score

The numerical average obtained by dividing the sum of all scores by the number of scores.