Determine Whether the Samples Are Independent or Dependent Construct A $95 \%$

question 30

Multiple Choice

Determine whether the samples are independent or dependent.
-Two types of flares are tested and their burning times are recorded. The summary statistics are given below. $\begin{array}{|ll|}\hline \frac{\text { Brand } \mathrm{X}}{\mathrm{n}=35} & \underline{\text { Brand } \mathrm{Y}} \\\overline{\mathrm{x}}=19.4 \mathrm{~min} & \overline{\mathrm{x}}=15.1 \mathrm{~min} \\\mathrm{~s}=1.4 \mathrm{~min} & \mathrm{~s}=0.8 \mathrm{~min} \\\hline\end{array}$

Construct a $95 \%$ confidence interval for the differences between the mean burning time of the brand $X$ flare and the mean burning time of the brand $Y$ flare.

• A) \(3.5 \mathrm {~min} < \mu \mathrm { X } - \mu \mathrm { Y } < 5.1 \mathrm {~min}\)
• B) \(3.2 \mathrm {~min} < \mu \mathrm { X } = \mu \mathrm { Y } < 5.4 \mathrm {~min}\)
• C) \(3.6 \mathrm {~min} < \mu \mathrm { X } - \mu \mathrm { Y } < 5.0 \mathrm {~min}\)
• D) \(3.8 \mathrm {~min} < \mu \mathrm { X } - \mu \mathrm { Y } < 4.8 \mathrm {~min}\)

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Definitions:

Case Study Method

A research strategy that involves an in-depth investigation of a single subject, group, or event to explore causation in order to find underlying principles.

In-depth Investigation

A comprehensive and detailed examination of a subject or issue, aiming to uncover deeper insights or facts.

Naturalistic Observation Method

A research methodology where subjects are observed in their natural environment without any manipulation by the observer.

Careful Surveillance

The meticulous observation or monitoring of behaviors, activities, or information for the purpose of influence, management, or protection.