7. Two methods of extracting juice from an orange are to be compared. Eight oranges are halved. One half of each orange is chosen at random and allocated to Method \(A\) and the other half is allocated to Method \(B\). The amounts of juice extracted, in ml , are given in the table.
| \cline { 2 - 9 }
\multicolumn{1}{c|}{} | Orange |
| \cline { 2 - 9 }
\multicolumn{1}{c|}{} | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| Method \(A\) | 29 | 30 | 26 | 25 | 26 | 22 | 23 | 28 | |
| Method \(B\) | 27 | 25 | 28 | 24 | 23 | 26 | 22 | 25 | |
One statistician suggests performing a two-sample \(t\)-test to investigate whether or not there is a difference between the mean amounts of juice extracted by the two methods.
- Stating your hypotheses clearly and using a \(5 \%\) significance level, carry out this test.
(You may assume \(\bar { x } _ { A } = 26.125 , s _ { A } ^ { 2 } = 7.84 , \bar { x } _ { B } = 25 , s _ { B } ^ { 2 } = 4\) and \(\sigma _ { A } ^ { 2 } = \sigma _ { B } ^ { 2 }\) )
Another statistician suggests analysing these data using a paired \(t\)-test. - Using a \(5 \%\) significance level, carry out this test.
- State which of these two tests you consider to be more appropriate. Give a reason for your choice.