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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 “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.

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Most popular questions from this chapter

t Test Exercise 2 refers to a t test. What is the t test? Why is the letter t used? What is unrealistic about the z test methods in Part 2 of this section?

Interpreting Power For the sample data in Example 1 “Adult Sleep” from this section, Minitab and StatCrunch show that the hypothesis test has power of 0.4943 of supporting the claim that μ<7 hours of sleep when the actual population mean is 6.0 hours of sleep. Interpret this value of the power, then identify the value of βand interpret that value. (For the t test in this section, a “noncentrality parameter” makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)

Calculating Power Consider a hypothesis test of the claim that the Ericsson method of gender selection is effective in increasing the likelihood of having a baby girl, so that the claim is p>0.5. Assume that a significance level of α= 0.05 is used, and the sample is a simple random sample of size n = 64.

a. Assuming that the true population proportion is 0.65, find the power of the test, which is the probability of rejecting the null hypothesis when it is false. (Hint: With a 0.05 significance level, the critical value is z = 1.645, so any test statistic in the right tail of the accompanying top graph is in the rejection region where the claim is supported. Find the sample proportion in the top graph, and use it to find the power shown in the bottom graph.)

b. Explain why the green-shaded region of the bottom graph represents the power of the test.

Final Conclusions. In Exercises 25–28, use a significance level of α= 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: The mean pulse rate (in beats per minute) of adult males is 72 bpm. The hypothesis test results in a P-value of 0.0095.

Testing Hypotheses. In Exercises 13–24, 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.

How Many English Words? A simple random sample of 10 pages from Merriam-Webster’s Collegiate Dictionary is obtained. The numbers of words defined on those pages are found, with these results: n = 10, x = 53.3 words, s = 15.7 words. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.0 words. Assume a normally distributed population. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.0 words. What does the result suggest about the claim that there are more than 70,000 defined words?
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