Question

Evaluate, from both a mathematical and a statistical perspective, the statement: 5 = 4.

Answer 1

Mathematical statistical perspective-

From mathematical perspective, this statement is a total nuisance and has no validity.

Statistical perspective-

From statistical perspective, this statement may have a meaning. Let us elaborate with an example.

Suppose, for any population value of a parameter is expected to be 4. We have to verify it using some set of sample data.

We have to test for null hypothesis

against the alternative hypothesis

We have few sample units drawn from that population. We wish to estimate value of that same parameter from sample data.

Suppose, estimated value of our sample statistic is 5. In such instance, we may reject the null hypothesis or not depending upon other variables like standard error, level of significance etc.

There may be instances that we fail to reject our null hypothesis when

• , level of significance of the test.
• 

In such instance, although we obtained estimate of the parameter as 5 using sample data, we arrive to a conclusion that population parameter does not differ from 4.

This situation may be treated as an example of the given statement'5=4'. Basically due to approximating nature of statistics, we obtained such a result.