In any salmon population, body mass varies. This is a form of continuous variation. Explain what continuous variation means and how it may arise.
Scientists investigated whether injection of very young non-GM salmon with recombinant growth hormone could increase the growth rate of the salmon. The scientists used two groups of non-GM salmon: a control group of salmon that were not injected with recombinant growth hormone; an experimental group of salmon that were injected with $1.0\,\mu\text{g}$ of recombinant growth hormone at the start of the experiment and once a week for the next six weeks. The mean body mass of the salmon in the two groups at the start of the experiment was the same ($5.3\,\text{g}$). After six weeks, the body mass of every salmon was measured again. The results are summarised in Table 3.1. A student decided that a $t$-test should be performed on the results shown in Table 3.1.
Calculate $t$ for the data in Table 3.1 by applying the $t$-test formula: $t = \dfrac{|\bar{x}_1 - \bar{x}_2|}{\sqrt{\left(\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}\right)}}$. Give your answer to two decimal places. Show your working.
The critical value at $p = 0.05$ for these data is $2.01$. The student used the results in Table 3.1 and the $t$-test to conclude that injections of recombinant growth hormone cause an increase in the growth rate of the non-GM salmon. Comment on how well the student's conclusion can be supported.
Suggest one advantage, apart from cost, of farming GM salmon that produce greater quantities of growth hormone rather than farming non-GM salmon that are injected with recombinant growth hormone each week.