Question

Uncertainty True or false: If correct methods of hypothesis testing are used with a large simple random sample that satisfies the test requirements, the conclusion will always be true.

Short answer

It is false that after applying the correct method to test a claim with a sufficiently large sample, it will always result in a conclusion that is true.

Step-by-step solution

Given information

The following statement is considered:

If correct methods of hypothesis testing are used with a large simple random sample that satisfies the test requirements, the conclusion will always be true.

Conclusion of the test

The statement “the conclusion will always be true” denotes the rejection of the null hypothesis.

The conclusion of a hypothesis test depends on the characteristics of the data values of the sample.

A sufficiently large sample may have statistics that are quite extreme which can result in a very small p-value and hence, the rejection of the null hypothesis.

Conversely, if the sample is large, but the p-value comes out to be greater than the significance level, then the null hypothesis is failed to reject.

Therefore, even if the sample follows all the requirements, there can be a case of failure to reject the null hypothesis, and thus, the conclusion will not be true.