3 Scientists are studying the effects of exercise on LDL blood cholesterol levels. Over a three-month period, a large group of people exercised for 20 minutes each day. For a randomly chosen sample of 10 of these people, the LDL blood cholesterol levels were measured at the beginning and the end of the three-month period. The results, measured in suitable units, are as follows.
| \cline { 2 - 12 }
\multicolumn{1}{c|}{} | | Person | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) | \(I\) |
| \multirow{2}{*}{} | Beginning | 72 | 84 | 120 | 90 | 102 | 135 | 64 | 75 | 80 | 88 |
| \cline { 2 - 12 } | End | 64 | 76 | 105 | 92 | 105 | 115 | 67 | 75 | 75 | 84 |
- Test, at the \(2.5 \%\) significance level, whether there is evidence that the population mean LDL blood cholesterol level has reduced by more than 2 units after the three-month period.
- State any assumption that you have made in part (a).
\includegraphics[max width=\textwidth, alt={}, center]{b6635fbc-3c9d-4f93-b51a-b1cbd71ddbb1-06_399_1383_269_324}
As shown in the diagram, the continuous random variable \(X\) has probability density function f given by
$$f ( x ) = \begin{cases} m x & 0 \leqslant x \leqslant 2
\frac { k } { x ^ { 2 } } + c & 2 \leqslant x \leqslant 6
0 & \text { otherwise } \end{cases}$$
where \(m , k\) and \(c\) are constants.