In the following problem: Set up the null hypothesis and the alternative hypothe

Question

In the following problem: Set up the null hypothesis and the alternative hypothesis. Test the hypothesis. The composition of the earths atmosphere may have changed over time. To try to discover the nature of the atmosphere long ago, we can examine the gas in bubbles inside ancient amber. Amber is tree resin that, has hardened and been trapped in rocks. The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed. Measurements on specimens of amber from the late Cretaceous era (75 to 95 million years ago) give these percents of nitrogen: 63.4 65 64.4 63.3 54.8 64.5 60.8 49.1 51 Assume (this is not yet agreed on by experts) that these observations are an SRS from the late Cretaceous atmosphere. Test the hypothesis that the mean percent of nitrogen in ancient air is different than 57 percent at the 1% significance level.

Explanation / Answer

1) H0: mu=0.57 (mean percent of nitrogen in ancient air is same as that of 57%)

H1:mu not equal to 0.57 (mean percent of nitrogen in ancient air is different from 57%)

2) Compute 1-sample t test (small sample size, n<30, population standard deviation is unknwon)

t=(xbar-mu)/(s/sqrt n), where xbar is sample mean, mu is population mean, s is sample standard deviation and n is sample size.

=(0.60-0.57)/(0.0626/sqrt 9)

=1.44

p value at df=8 (df=n-1), and alpha=0.01 is 0.187828.

P value is not less than alpha, fail to reject null hypothesis. There is not sufficient sample evidence to conclude that mean percent of nitrogen in ancient air is different from 57%.

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