7. A grocer receives deliveries of cauliflowers from two different growers, \(A\) and \(B\). The grocer takes random samples of cauliflowers from those supplied by each grower. He measures the weight \(x\), in grams, of each cauliflower. The results are summarised in the table below.

1. Show, at the \(10 \%\) significance level, that the variances of the populations from which the samples are drawn can be assumed to be equal by testing the hypothesis \(\mathrm { H } _ { 0 } : \sigma _ { A } ^ { 2 } = \sigma _ { B } ^ { 2 }\) against hypothesis \(\mathrm { H } _ { 1 } : \sigma _ { A } ^ { 2 } \neq \sigma _ { B } ^ { 2 }\).
   (You may assume that the two samples come from normal populations.)
   (6) The grocer believes that the mean weight of cauliflowers provided by \(B\) is at least 150 g more than the mean weight of cauliflowers provided by \(A\).
2. Use a \(5 \%\) significance level to test the grocer's belief.
3. Justify your choice of test.