Z-test with Alpha Level A medical company has performed and experiment using to treat me to groups: cancer patients taking a new drug (treatment group) and cancer patients taking a placebo (control group). They want to compare the proportion of patient showing improvement in the drug treatment group to the proportions of patients showing improvement in the control group. Because the new drug has severe side effects, they only want to begin production if it can be shown it has a significant improvement in patients. Given these concerns, which of the following inferntial procedures would be the best choice?
A. One proportion Z test with alpha level of 5%
B. One proportion Z test with alpha level of 10%
C. One proportion Z test with alpha level of 20%
D. Two proportion Z test with alpha level of 5%
E. Two proportion Z test with alpha level of 10%
My Answer
I Strongly believe the answer to be D, a Two-Proportion z-test with alpha level of 5%
My Reasoning
It’s should be a two-proportion z-test since we are looking at two different groups & the alpha level should be this lowest possible, which would be 5% since we are rear hung about a live saving medicine. The margin of error needs to be low as possible.
Thoughts on this
 A: We can immediately dismiss options (A), (B), and (C), because there are two distinct proportions involved--the proportion of responders in the treatment group, and the proportion of responders in the placebo group.
The question of significance level is, in the language of biostatistics, a matter of consumer risk (i.e., the patient) versus sponsor risk (i.e., the drug company).  Consumer risk is the possibility of taking a drug that is unsafe or not effective.  Sponsor risk is the possibility of failing to detect an effective treatment, thus wasting resources.  The significance level $\alpha$ controls consumer risk.  The power, $1-\beta$, quantifies the sponsor's risk.
The smaller we choose $\alpha$, the less tolerant we are of Type I error--i.e., erroneously concluding that the treatment is effective, when in fact it is not.  The burden of evidence for treatment efficacy must be greater as we decrease $\alpha$.  Therefore, this choice determines the extent to which we are willing to be wrong about approving an ineffective treatment regimen and prescribing it to patients.  As such, the best answer is (D), since (E) has a larger $\alpha$.
