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S2 hypothesis question

a) b) c) are all fine
for part d) got confused though

For part c) was using Y~Bin(0.25) so could use the binomial tables. For part d) it suggests in mark scheme using this method P(Y greater/equal to 20-c) less than/equal to 0.01.
can someone explain this.
thanks

Q. (June 05 paper)
A drugs company claims that 75% of patients suffering from depression recover when treated with a new drug.
A random sample of 10 patients with depression is taken from a doctor’s records.

(a)Write down a suitable distribution to model the number of patients in this sample who recover when treated with the new drug.

Given that the claim is correct,

(b) find the probability that the treatment will be successful for exactly 6 patients.

The doctor believes that the claim is incorrect and the percentage who will recover is lower. From her records she took a random sample of 20 patients who had been treated with the new drug. She found that 13 had recovered.

(c)Stating your hypotheses clearly, test, at the 5% level of significance, the doctor’s belief.

d)From a sample of size 20, find the greatest number of patients who need to recover from the test in part (c) to be significant at the 1% level

Reply 1

Popa Dom

Sorry to 'jack your thread somewhat, but this question confuses me. For part c), why does the mark scheme use P(X<=13) when the doctor thinks the probability is lower? Surely to verify H₀ you should be using P(X>=13), as thats the boundary of the critical region you would be looking at.

Anyway to answer your question, because you cant use the tables for B(20,0.75), you have to look at the number of cases that havent recovered with B(20,0.25). If c patients recovered and there were 20 patients, that means 20-c patients didnt recover, so you use that.