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

question 29

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 coach uses a new technique in training middle distance runners. The times for 9 different athletes to run 800 meters before and after this training are shown below. $\begin{array}{r|ccccccccc}\text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } \\\hline \text { Time before training (seconds) } & 115.2 & 120.9 & 108.0 & 112.4 & 107.5 & 119.1 & 121.3 & 110.8 & 122.3 \\\hline \text { Time after training (seconds) } & 116.0 & 119.1 & 105.1 & 111.9 & 109.1 & 115.2 & 118.5 & 110.7 & 120.9\end{array}$
Construct a $99 \%$ confidence interval for the mean difference of the "before" minus "after" times.

• A) \(- 0.76 < \mu _ { \mathrm { d } } < 3.20\)
• B) \(- 0.85 < \mu _ { \mathrm { d } } < 3.29\)
• C) \(- 0.54 < \mu _ { \mathrm { d } } < 2.98\)
• D) \(- 0.82 < \mu _ { \mathrm { d } } < 3.26\)

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Definitions:

Inventory Holding Gain

An increase in the value of inventory over time, typically due to inflation or increased demand, before the inventory is sold.

FIFO Earnings

The net income calculated using the First-In, First-Out method of inventory valuation, assuming the first items purchased are the first sold.

Inventory Units

Inventory units are the measurable quantities of goods or materials on hand, stored or processed by a business, intended for sale or production.

Goods Available

The total quantity of goods on hand for sale during a specific period, including both beginning inventory and purchases made.