Can someone check my answers for the following questions? Thanks.

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.

H0: p=.64

H1: p>.64

alpha = 5%

p-hat - 87/125 = .696

If H0 is true:

z=(.696-.64)/(√.36/125)

alpha = 5% = 1.645

The z-score of 1.304 lies within the range of 1.645 so we don't have sufficient evidence that the new approach is better so we don't reject H0.

b) What is the P-value for the test in part (a)?

p-value = 1-.8485 = .1515

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?

90% = k = 1.645

e = .05

p = .696

n=.696(1-.696)x(1.645/.05)^2

= 229