Construct the Indicated Confidence Interval for the Difference Between the Two

question 18

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.
-Two types of flares are tested and their burning times are recorded. The summary statistics are given below.

$\begin{array}{ll}\text { Brand } X&\text { Brand } Y\\\mathrm{n}=35 & \mathrm{n}=40 \\\overline{\mathrm{x}}=19.4 \mathrm{~min} & \overline{\mathrm{x}}=15.1 \mathrm{~min} \\\mathrm{~s}=1.4 \mathrm{~min} & \mathrm{~s}=0.8 \mathrm{~min}\end{array}$
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) \(3.8 \mathrm {~min} < \mu X - \mu Y < 4.8 \mathrm {~min}\)
• B) \(3.5 \mathrm {~min} < \mu _ { X } - \mu _ { Y } < 5.1 \mathrm {~min}\)
• C) \(3.6 \mathrm {~min} < \mu _ { X } - \mu _ { Y } < 5.0 \mathrm {~min}\)
• D) \(3.2 \mathrm {~min} < \mu _ { X } - \mu _ { Y } < 5.4 \mathrm {~min}\)

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Definitions:

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A 1765 British law imposing a tax on all paper documents in the American colonies, leading to widespread protest and contributing to the American Revolution.

Sugar Act

A law enacted by the British Parliament in 1764 aiming to raise revenue from the American colonies by imposing a tax on sugar and molasses imported from non-British territories.

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A legal procedure in which a jury made up of citizens determines the outcome of a case, based on evidence presented, in both civil and criminal trials.