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 three 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. What is the explanation for this? Explain in detail.

The low sample size results in a lower power of test which in turn gives a not statistically significant result.

Step-by-step explanation:

The hypothesis that would have been defined by the medical researcher is:

H₀: The mean survival time after diagnosis on the standard treatment is two years, i. e. μ = 2.

Hₐ: The mean survival time after diagnosis on the standard treatment is different from two years, i. e. μ ≠ 2.

The significance level of the test is α = 0.10.

The sample taken by the medical researcher is of size, n = 3.

It is provided that the average survival time for the sample is 4 years.

Even then the null hypothesis was not rejected, i, e,. the results were not statistically significant.

This can be explained by the concept of power of test.

The power of test is defined as the probability of rejecting a false null hypothesis.

The power of test is affected by two things:

The sample size (n) must be large. The significance level of the test must also be large.

The significance level of the test is 0.10. This value of α is quite large.

The sample size is n = 3. The sample size is too small.

Because of the small sample size the power of the test must have been lower.

Thus, resulting in a statistically insignificant conclusion.

Thus, as the low sample size results in a lower power of test which in turn gives a not statistically significant result.