Question

Suppose that, using standard treatments, 60% of patients completely recover from a disease. A new treatment is used on a random sample of 800 individuals, and 513 completely recover. Is this evidence, at the 5% level of significance, that this new treatment can improve the recovery rate? Do a complete hypothesis test, and show all work. (included the formula)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.6
Alternative Hypothesis, Ha: p > 0.6

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6413 - 0.6)/sqrt(0.6*(1-0.6)/800)
z = 2.38

P-value Approach
P-value = 0.0087
As P-value < 0.05, reject the null hypothesis.