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:

Stimulus

A detectable change in the internal or external environment that can elicit or evoke a physiological response from an organism.

Consumer Behavior

The study of individuals, groups, or organizations and the processes they use to select, secure, use, and dispose of products, services, experiences, or ideas to satisfy needs and impacts on the consumer and society.

Cognitive Dissonance

A psychological phenomenon where there is discomfort from holding conflicting beliefs, values, or attitudes, often leading to behavior change.

Ritual Consumption

The patterns of behaviors and customs involved in the purchasing and use of products or services in a way that holds symbolic meaning.