11 A particular dietary supplement, when taken for a period of 1 month, is claimed to increase lean body mass of adults by an average of 1 kg . A researcher believes that this claim overestimates the increase. She selects a random sample of 10 adults who then each take the supplement for a month. The increases in lean body masses in kg are as follows.
$$\begin{array} { l l l l l l l l l l }
- 0.84 & - 0.76 & - 0.16 & 0.43 & 1.31 & 1.32 & 1.47 & 1.64 & 1.93 & 2.14
\end{array}$$
A Normal probability plot and the \(p\)-value of the Kolmogorov-Smirnov test for these data are shown below.
\includegraphics[max width=\textwidth, alt={}, center]{77eabbd6-a058-457f-9601-d66f3c2db005-09_575_1485_689_242}
- The researcher decides to carry out a hypothesis test in order to investigate the claim.
Comment on the type of hypothesis test that should be used. You should refer to
- The Normal probability plot
- The \(p\)-value of the Kolmogorov-Smirnov test
- Carry out a test at the \(5 \%\) significance level to investigate whether the researcher's belief may be correct.
- If the Normal probability plot had been different, giving a \(p\)-value of 0.65 for the KolmogorovSmirnov test, a different procedure could have been used to investigate the researcher's belief.
- State what alternative test could have been used in this case.
- State what the hypotheses would have been.