1. When considering the Patient Satisfaction data, will we use the normal distribution or the t distribution to set up confidence intervals? Clearly state the reasons for your decision and state the conditions that must hold for you to use the suggested distribution. (2 marks)

1. Test whether the Patient satisfaction score follows an approximate normal distribution. If the data does not follow a normal distribution indicate how the data can be normalised and show if the method you used was effective. Clearly describe your steps and reasoning. (5 marks)

1. Calculate an appropriate estimate of the mean and its associated 95% confidence interval based on this sample. Cite your answers to 1 decimal place. (2 marks)Note: in practice, the final mean and 95% CI is always presented in the original scale (patient satisfaction score). In question 1c) you are not required to do so.

1. Select a random sample from this data set, containing 8 data points, and set up the 95% confidence intervals for this smaller sample. Indicate how this 95% confidence interval compares to the 95% confidence interval in question (c). Give a reason to support your answer. (2 marks).

1. If you were to re-import the data and draw another sample of 8 participants. Would your 95% confidence interval be the same as in question d? Give reasons to support your answer. (1 mark)

ID	Patient Satisfaction Score
1	15.4
2	27.5
3	33.0
4	46.2
5	59.4
6	18.7
7	28.6
8	34.1
9	47.3
10	59.4
11	22.0
12	28.6
13	34.1
14	50.6
15	69.3
16	23.1
17	28.6
18	35.2
19	52.8
20	73.7
21	24.2
22	29.7
23	38.5
24	57.2
25	91.3
26	26.4
27	47.3
28	34.1