5. A laboratory carrying out screening for a certain blood disorder claims that the average time taken for test results to be returned is 38 hours. A reporter for a national newspaper suspects that the results take longer, on average, to be returned than claimed by the laboratory. The reporter finds the time, \(x\) hours, for 50 randomly selected results, in order to conduct a hypothesis test. The following summary statistics were obtained. $$\sum x = 2163 \quad \sum x ^ { 2 } = 98508$$

1. Calculate the \(p\)-value for the reporter's hypothesis test, and complete the test using a \(5 \%\) level of significance. Hence write a headline for the reporter to use.
2. Explain the relevance or otherwise of the Central Limit Theorem to your answer in part (a).
3. Briefly explain why a random sample is preferable to taking a batch of 50 consecutive results.
4. On another occasion, the reporter took a different random sample of 10 results.
   1. State, with a reason, what type of hypothesis test the reporter should use on this occasion.
   2. State one assumption required to carry out this test.