Final answer:
A statistical test is needed to determine if the observed mortality rate with the experimental drug of 17.9% is significantly less than the expected rate of 23%. A hypothesis test, such as a Chi-square or Z-test, will help ascertain whether there is strong evidence that the drug reduces mortality rates, considering Type I and Type II errors.
Step-by-step explanation:
The question revolves around determining if an experimental drug significantly reduces the mortality rate from a certain type of cancer. Given that the expected death rate is 23% during the first year, and the observed death rate with the experimental drug was 15 out of 84 patients, which is approximately 17.9%, we would perform a hypothesis test to analyze if this is a significant reduction.
For this case, the null hypothesis (H0) is that the drug does not reduce the mortality rate, meaning the death rate is still 23%. In contrast, the alternative hypothesis (H1) is that the drug does reduce the mortality rate, meaning the death rate is less than 23%. To address the question posed, we would typically use a statistical test, such as a Chi-square test or a Z-test for proportions, to determine if the observed rate of 17.9% is significantly less than the expected rate of 23%.
If the p-value calculated from the test is below a predetermined significance level (commonly 0.05), we can conclude that there is strong evidence that the experimental drug reduces the mortality rate. Otherwise, we would not reject the null hypothesis.
It is also important to note that in making conclusions, there can be Type I and Type II errors. A Type I error would be claiming the drug is effective when it is not, and a Type II error would be failing to recognize the drug's effectiveness when it actually is effective. The question presented does not provide enough information to calculate the exact p-value or to make a final conclusion on the effectiveness of the drug without performing the precise statistical test.