Ancient air 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 $9$specimens of amber from the late Cretaceous era ($75to95$ million years ago) give these percents of nitrogen:

$63.465.064.463.354.864.560.849.151.0$Explain why we should not carry out a one-sample t test in this setting.

The gas in bubbles within amber should be a sample of the atmosphere at the time the amber was formed.

Measurements on $9$specimens of amber from the late Cretaceous era ($75to95$ million years ago) give these percents of nitrogen:

$63.465.064.463.354.864.560.849.151.0$

Test for $\mu$:

$\mu$= mean percent of nitrogen in the air during the cretaceous era

Conditions: not a random sample, but representative of air in the cretaceous era independent:$9$samples. $10\%$fall air samples from cretaceous era.

Normal:$n=9<30$

Strong left skew, but no outliers. proceed with caution.

localid="1650695039374" $$\begin{gathered} H_0:\mu =78.1 \\ {H}_a:\mu \ne 78.1 \\ t=-8.878 \\ p-value=2.05\times {10}^{-5} \\ df=8 \end{gathered}$$

We reject$H_0,$because p-value is less than $\alpha$. We have sufficient evidence to say the mean percent of nitrogen in the air during the late Cretaceous era was less than $78.1\%.$