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Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 10 - Problem 10.117
Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 10 - Problem 10.117

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# Lord Rayleigh was one of the earliest scientists to study the density of nitrogen. In

ISBN: 9780495110811 47

## Solution for problem 10.117 Chapter 10

Mathematical Statistics with Applications | 7th Edition

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Problem 10.117

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 Rayleighs measurements18 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 = .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.

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Section 6: Statistics in Sports Stat 2220, Espey ➢ Random Variable: a variable with different outcomes that each assume a numerical value ○ Represented with Y ○ Discrete RV: countable ○ Continuous RV: measured on a continuous scale (decimals can be used) ➢ Binomial Random Variable: How many times one two possible outcomes occurs after a series of independent trials ○ Ex: When shooting a basketball, there are two outcomes: making the basket or missing it. We decide to count how many baskets are made after four shots (four independent trials). The binomial random variable Y is the amount of baskets made after these trials. ○ To find the probability of a value of Y

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