the proportion of individuals responding to the standard treatment for a childhood blood disorder has been constant over a number of years, at 64%. A new treatment is being trialled and early results show that of the 125 patients exposed to the new treatment, 87 have responded.

a) can we claim a new improved treatment? conduct an appropriate hypothesis test at a 5% significance level using a critical value approach.

b) what is the P-Value for the test in part a)?

c) if we wanted to be 90% sure that our sample proportion was within 0.05 of the true response rate for the new treatment, how many randomly-selected patients would we need to treat?

thank you for your help