Statistics / Mathematical Statistics with Applications 7 / Chapter 10 / Problem 117SE

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Lord Rayleigh was one of the earliest scientists to study

Chapter 10, Problem 117SE

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Lord Rayleigh was one of the earliest scientists to study the density of nitrogen. In his studies, he noticed something peculiar. The nitrogen densities produced from chemical compounds tended to be smaller than the densities of nitrogen produced from the air. Lord Rayleigh's measurements ${\ }^{18}$ are given in the following table. These measurements correspond to the mass of nitrogen filling a flask of specified volume under specified temperature and pressure.

Compound Chemical	Atmosphere
$2.30143$	$2.31017$
$2.29890$	$2.30986$
$2.29816$	$2.31010$
$2.30182$	$2.31001$
$2.29869$	$2.31024$
$2.29940$	$2.31010$
$2.29849$	$2.31028$
$2.29889$	$2.31163$
$2.30074$	$2.30956$
$2.30054$

a For the measurements from the chemical compound, $y^{-}=2.29971$ and $s=.001310$; for the measurements from the atmosphere, $y^{-}=2.310217$ and $s=.000574$. Is there sufficient evidence to indicate a difference in the mean mass of nitrogen per flask for chemical compounds and air? What can be said about the $p$ -value associated with your test?

b Find a $95\%$ confidence interval for the difference in mean mass of nitrogen per flask for chemical compounds and air.

c Based on your answer to part (b), at the $\alpha{}=.05$ level of significance, is there sufficient evidence to indicate a difference in mean mass of nitrogen per flask for measurements from chemical compounds and air?

d Is there any conflict between your conclusions in parts (a) and (b)? Although the difference in these mean nitrogen masses is small, Lord Rayleigh emphasized this difference rather than ignoring it, and this led to the discovery of inert gases in the atmosphere.

Equation transcription:

${y}^{-}=2.29971$