The average survival time after diagnosis for a certain type of cancer on the standard treatment is two years. A medical researcher is working on a new treatment. In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of four years. Although the survival time doubled, the results are not statistically significant, even at the 0.10 significance level, because: the calculation was in error; the researchers forgot to include the sample size. the placebo effect is present, which limits statistical significance. although the survival time has doubled, the actual increase is really two years. the sample size is small.

The answer is the last one: the sample size is too small. Since we only got 3 subjects to test, maybe one of them could live for a long time after the diagnosis of Cacer and that made the average survival time go up by a lot.

In order to obtain results with a significance level higher, you need a sample size of at least 20 subjects.

Now lets see why other options wouldnt be good answers:

For a small amount of subjects, it is unlikely to have errors in caculation
The sample size is given
We are not given information about the treatment and we dont even know if the subjects feel more confident with the new treatment. Also, if a Placebo effect works regularly, it shouldnt limit statistical sifgnificance
An increase in 2 years is huge in comparison with the previous survival time.