This is also on the university side of this forum.
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