3. Awena has a large data set of body measurements, and she wants to investigate relationships between body dimensions. In this particular investigation, she is testing for a correlation between forearm girth and bicep girth. The diagrams below show how to measure these.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f47b2ff-f954-42ec-8ecc-fc64313a7b89-06_499_590_534_276}
\captionsetup{labelformat=empty}
\caption{Forearm girth}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f47b2ff-f954-42ec-8ecc-fc64313a7b89-06_499_591_534_1194}
\captionsetup{labelformat=empty}
\caption{Bicep girth}
\end{figure}
- Why is it appropriate for Awena to use a one-tailed test?
Awena takes a random sample of size 11 from her data set and plots the following scatter diagram.
\includegraphics[max width=\textwidth, alt={}, center]{8f47b2ff-f954-42ec-8ecc-fc64313a7b89-07_937_1431_420_312} - Using the computer output above, carry out a one-tailed significance test on the sample product moment correlation coefficient at the \(0 \cdot 5 \%\) level.
- Blodwen also has access to the same large data set. She decides to do the same test using all of the 507 available data points. Her results are shown below.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Forearm girth versus Bicep girth}
\includegraphics[alt={},max width=\textwidth]{8f47b2ff-f954-42ec-8ecc-fc64313a7b89-08_933_1504_477_276}
\end{figure}
- State the problem Blodwen will encounter when attempting to use statistical tables for her test.
- How should Blodwen deal with this problem?
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