8 A student doing a school project wants to test a claim which she read in a newspaper that drinking a cup of tea will improve a person's arithmetic skills.
She chooses 13 students from her school and gets each of them to drink a cup of tea. She then gives each of them an arithmetic test. She knows that the average score for this test in students of the same age group as those she has chosen is 33.5.
The scores of the students she tests, arranged in ascending order, are as follows.
\(\begin{array} { l l l l l l l l l l l l l } 26 & 28 & 29 & 30 & 31 & 32 & 34 & 42 & 49 & 54 & 55 & 56 & 61 \end{array}\)
The student decides to use software to draw a Normal probability plot for these data, and to carry out a Normality test as shown in Fig. 8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3a89edc4-ac93-4691-ade8-4d4665b55202-09_536_1234_792_244}
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\caption{Fig. 8}
\end{figure}
- The student uses the output from the software to help in deciding on a suitable hypothesis test to use for investigating the claim about drinking tea.
Explain what the student should conclude. - The student's teacher agrees with the student's choice of hypothesis test, but says that even this test may not be valid as there may be some unsatisfactory features in the student's project. Give three features that the teacher might identify as unsatisfactory.
- Assuming that the student's procedures can be justified, carry out an appropriate test at the \(5 \%\) significance level to investigate the claim about drinking tea.