5 A student is investigating possible association between the amount of coffee that an adult drinks each day and the number of hours that they remain awake each day. In an initial investigation, a random sample of 8 adults is selected. The student obtains the following information from each of these adults: the amount of coffee that they drink each day and the number of hours that they remain awake each day. The student analyses the data and finds that the associated product moment correlation coefficient is 0.6030 .

1. State one assumption that must be made for a hypothesis test based on the product moment correlation coefficient to be carried out. For the remainder of this question you may assume that this assumption is true.
2. Carry out a test at the \(5 \%\) significance level to investigate whether there is any correlation between amount of coffee drunk and number of hours awake. The student conducts a second investigation which is similar to the first but this time based on a random sample of 30 adults. The product moment correlation coefficient for the new data is 0.5487 . The student carries out an equivalent hypothesis test to the one carried out in part (b), again using a 5\% significance level.
3. Identify any differences between the two tests and their results. You do not need to restate the hypotheses or explain the conclusion in context.
4. You may assume the following guidelines for considering effect size.

   Product moment correlation coefficient	Effect size
   0.1	Small
   0.3	Medium
   0.5	Large

   Explain briefly why the results of the student's second investigation are likely to be more reliable than the results of the initial investigation.