Question

The composition of the earth's 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    65.0    64.4    63.3    54.8    64.5    60.8    49.1    51.0

Assume (this is not yet agreed on by experts) that these observations are an SRS from the late Cretaceous atmosphere.

Use a 98% confidence interval to estimate the mean percent of nitrogen in ancient air.

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Answer 1

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   6.2553  
Sample Size ,   n =    9  
Sample Mean,    x̅ = ΣX/n =    59.5889  
          
Level of Significance ,    α =    0.02          
degree of freedom=   DF=n-1=   8          
't value='   tα/2=   2.8965   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   6.2553   / √   9   =   2.085096
margin of error , E=t*SE =   2.8965   *   2.08510   =   6.039395
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    59.59   -   6.039395   =   53.549494
Interval Upper Limit = x̅ + E =    59.59   -   6.039395   =   65.628284
98%   confidence interval is (   53.55   < µ <   65.63   )

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