Paired t-test

1. A researcher set up a trial to assess the effect that a food supplement has on the increase in weight of Herdwick lambs. The researcher randomly selected 8 sets of twin lambs. One of each set of twins was given the food supplement and the other had no food supplement. The gain in weight, in kg, of each lamb over the period of the trial was recorded.

1. State why a two sample \(t\)-test is not suitable for use with these data.
2. Suggest 2 other factors about the lambs that the researcher may need to control when selecting the sample.
3. State one assumption, in context, that needs to be made for a paired \(t\)-test to be valid. For a pair of twin lambs, the random variable \(W\) represents the weight gain of the lamb given the food supplement minus the weight gain of the lamb not given the food supplement.
4. Using the data in the table, calculate a \(98 \%\) confidence interval for the mean of \(W\) Show your working clearly. The researcher believes that the mean of \(W\) is greater than 200 g
5. Stating your hypotheses clearly, use your confidence interval to explain whether or not there is evidence to support the researcher's belief.

A national athletics coach suspects that, on average, 200-metre runners' indoor times exceed their outdoor times by more than 0.1 seconds. In order to test this, the coach randomly selects eight 200-metre runners and records their indoor and outdoor times. The results, in seconds, are shown in the table. Stating suitable hypotheses and any necessary assumption that you make, test the coach's suspicion at the 2.5% level of significance. [10]