Dr Z was notified that for a particular procedure his compli

Dr. Z was notified that for a particular procedure, his complication rate of 20% for his years of doing the procedure was too high. So he took a one month remedial course. His complication rate is now 15% based on a sample size of 36. Has he actually improved? Please state your null and alternative, your test statistic, the p-value, and your conclusion.

Solution

The test hypothesis:

Ho: p=0.2 (i.e. null hypothesis)

Ha: p <0.2 (i.e. alternative hypothesis)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(0.15-0.2)/sqrt(0.2*0.8/36)

=-0.75

It is a left-tailed test.

So the p-value = P(Z<-0.75) =0.2266 (from standard normal table)

Assume that the significant level a=0.05

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can conclude that the rate is 20%