7 A researcher is investigating the actual lengths of time that patients spend with the doctor at their appointments. He plans to choose a sample of 12 appointments on a particular day.
- Which of the following methods is preferable, and why?
- Choose the first 12 appointments of the day.
- Choose 12 appointments evenly spaced throughout the day.
Appointments are scheduled to last 10 minutes. The actual lengths of time, in minutes, that patients spend with the doctor may be assumed to have a normal distribution with mean \(\mu\) and standard deviation 3.4. The researcher suspects that the actual time spent is more than 10 minutes on average. To test this suspicion, he recorded the actual times spent for a random sample of 12 appointments and carried out a hypothesis test at the 1\% significance level. - State the probability of making a Type I error and explain what is meant by a Type I error in this context.
- Given that the total length of time spent for the 12 appointments was 147 minutes, carry out the test.
- Give a reason why the Central Limit theorem was not needed in part (iii).