Question

Equivalent MethodsWhich of the following statements are true?

a.When testing a claim about a population mean$\mu$, theP-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.

b.When testing a claim about a population proportionp, theP-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.

c.When testing a claim about any population parameter, theP-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.

Short answer

Only option a. is true.

Step-by-step solution

Given information

Three statements about the conclusion of the claim obtained using the 3 different methods are provided.

Identifying the true statement

It is known that while testing a claim about the population proportion, the result obtained from the p-value and the critical method is not always the same as obtained from the confidence interval method.

While for testing a claim about the population mean, the result obtained from the p-value and the critical method is always the same as obtained from the confidence interval method.

On the basis of this knowledge, the following three statements are analysed:

• It is given thatwhen testing a claim about a population mean, theP-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.

As mentioned above, the given statement is true.

Thus, part a. is true.

• It is given thatwhen testing a claim about a population proportion, theP-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.

As mentioned above, the given statement is false.

Thus, part b. is false.

• It is given thatwhen testing a claim about any population parameter, theP-value method, critical value method, and confidence interval method are all equivalent in the sense that they always yield the same conclusions.

Since the above statement is not rye for the population proportion, the given statement is false.

Thus, part c. is false.

Therefore, only part a. is true.