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 (75 to 95 million years ago) give these percent of nitrogen:

63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0

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

A test statistic is a statistic utilized in statistical hypothesis testing. A hypothesis test is typically specified as far as a test statistic, considered as a numerical synopsis of an informational collection that decreases the information to one worth that can be utilized to play out the hypothesis test.

Given,

$\begin{array}{l}63.4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}65.0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}64.4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}63.3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}54.8\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}64.5\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}60.8\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}49.1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}51.0\end{array}$

We cannot carry out a one-sample t-test in this setting as a selection of the sample is done through a simple random technique and the sample size is $9$which is less than $30$. Hence the normality assumption is not satisfied.

Hence the selection of the sample is done through a simple random technique and we should not carry out a one-sample t test in this setting.