A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on 3 subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant, even at the 0.10 significance level. Which of the following explains the result? Select all that apply.
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.
The placebo effect is present, which limits statistical significance.
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.
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.
There is definitely not a difference if the p-value is that large.