A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis for the standard treatment is two years. So the null hypothesis is that average survival time after diagnosis is the same for the new treatment and the standard treatment. In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of 4.5 years. Even though the sample is small, the results are statistically significant at the 0.05 significance level. Consequently, she rejects the null hypothesis.

A. The alternative hypothesis could really be true but because the sample size is small, the power is very low so the researchers are likely to run an experiment whose results lead them to make a type II error.B. The placebo effect is present, which limits statistical significance.C. Although the survival time has doubled in the experiment, the statistical analysis proves that in reality the actual average survival time on the new treatment is only two years.D. The null hypothesis could be true and there is no difference between the new and standard treatments survival rate. The reason there is a difference in survival rates in this data set can be reasonably explained by chance selection of subjects.E. There is definitely not a difference if the p-value is that large.

Option A: The alternative hypothesis could really be true but because the sample size is small, the power is very low so the researchers are likely to run an experiment whose results lead them to make a type II error.

Option D: Inasmuch there is no statistical evidence to accept the null hypothesis. The null hypothesis could be true and there is no difference between the new and standard treatments survival rate.

Explanation:

Below are the options suitable for results:

Option A: The alternative hypothesis could really be true but because the sample size is small, the power is very low so the researchers are likely to run an experiment whose results lead them to make a type II error - Reason been that, as the sample size increase, so also does the power of the test increase. Therefore, because the power is too small, the researchers are likely to commit type 2 error.

Option D: Inasmuch there is no statistical evidence to accept the null hypothesis. The null hypothesis could be true and there is no difference between the new and standard treatments survival rate.