7 An analyst routinely examines bottles of hair shampoo in order to check that the average percentage of a particular chemical which the shampoo contains does not exceed the value of \(1.0 \%\) specified by the manufacturer. The percentages of the chemical in a random sample of 12 bottles of the shampoo are as follows.
\(\begin{array} { l l l l l l l l l l l } 1.087 & 1.171 & 1.047 & 0.846 & 0.909 & 1.052 & 1.042 & 0.893 & 1.021 & 1.085 & 1.096 \end{array} 0.931\)
The analyst uses software to draw a Normal probability plot for these data, and to carry out a Normality test as shown below.
\includegraphics[max width=\textwidth, alt={}, center]{c692fb20-436f-4bc1-89bd-10fdba41ceba-08_524_1539_694_264}
- The analyst is going to carry out a hypothesis test to check whether the average percentage exceeds 1.0\%.
Explain which test the analyst should use, referring to each of the following.
- The Normal probability plot
- The \(p\)-value of the Kolmogorov-Smirnov test
- In this question you must show detailed reasoning.
Carry out the test at the 5\% significance level.