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Chapter 8: Q10CQQ (page 356)

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

Expert verified

Only option a. is true.

Step by step solution

01

Given information

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

02

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.

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Most popular questions from this chapter

Confidence interval Assume that we will use the sample data from Exercise 1 鈥淰ideo Games鈥� with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < 渭< 191.4 sec, what should we conclude about the claim?

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