Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

question 135

Essay

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-Two types of flares are tested and their burning times are recorded. The summary statistics are given below.
Use a 0.05 significance level to test the claim that the burning times for Brand X flares have the same variance as
the burning times for Brand Y flares. $$\begin{array}{l}\frac { \text { Brand } X } { n = 35 } \quad \frac { \text { Brand } Y } { n = 41 }\\\bar { x } = 19.4 \mathrm {~min} \quad \bar { x } = 15.1 \mathrm {~min}\\\mathrm { s } = 1.4 \mathrm {~min} \quad \mathrm {~s} = 0.8 \mathrm {~min}\end{array}$$

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Definitions:

Applied Factory Overhead

Costs indirectly associated with manufacturing, including expenses such as utilities and management salaries, allocated to specific products or departments.

Direct Materials

Raw materials that are directly traceable to the manufacturing of a specific product.

Continuous Process

A production method used to manufacture, produce, or process materials without interruption.

Conversion Cost

The combined costs of direct labor and manufacturing overhead involved in transforming materials into finished goods.