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Chapter 8: Q7 (page 408)

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

Expert verified

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

01

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.

02

Conclusion of the test

The statement 鈥渢he conclusion will always be true鈥� 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.

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Most popular questions from this chapter

Interpreting Power Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.

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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a. Find the critical value(s).

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Exercise 17

Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

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Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

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