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# How do I answer this S2 question? watch

1. The question is from exercise 7C:Q11 - The national proportion of people experiencing complications after having a particular operation in hospitals is 20% A particular hospital decides to take a sample of size 20 from their records.

a) State all the possible numbers of patients with complications that would cause them to decide that their proportion of complications differs from the national figure at the 5% level of significance, ensuring that the probability in each tail is as near to 2.5% as possible.

The hospital finds that out of 20 such operations, 8 of their patients experienced complications.

b) Find critical regions, at the 5% level of significance to test whether or not their proportion of complications differs from the national proportion. The probability in each tail should be as near to 2.5% as possible.

For a) I got X=0 and X>8 but I'm not sure how to answer B as I though we had already worked out the critical regions in a).
2. (Original post by Parrotperson)
The question is from exercise 7C:Q11 - The national proportion of people experiencing complications after having a particular operation in hospitals is 20% A particular hospital decides to take a sample of size 20 from their records.

a) State all the possible numbers of patients with complications that would cause them to decide that their proportion of complications differs from the national figure at the 5% level of significance, ensuring that the probability in each tail is as near to 2.5% as possible.

The hospital finds that out of 20 such operations, 8 of their patients experienced complications.

b) Find critical regions, at the 5% level of significance to test whether or not their proportion of complications differs from the national proportion. The probability in each tail should be as near to 2.5% as possible.

For a) I got X=0 and X>8 but I'm not sure how to answer B as I though we had already worked out the critical regions in a).
For the first question your answer is slightly wrong, I'm fairly sure that it wants you to list all of the numbers that would be in the critical region so you would write x=0,9,10,11 etc. For the second question I would probably write the critical region is x=0 or x>8 (x>=9) so therefore x=8 is not in the critical region so there is insufficient evidence to reject the null hypothesis

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