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Chapter 8: Q. 9.53 (page 370)
Which provides stronger evidence against the null hypothesis, a P-value of or a P-value of ? Explain your answer.
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In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Requirements and Conclusions
a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?
b. It was stated that we can easily remember how to interpret P-values with this: “If the P is low, the null must go.” What does this mean?
c. Another memory trick commonly used is this: “If the P is high, the null will fly.” Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?
d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?
Testing Claims About Proportions. In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Medication Usage In a survey of 3005 adults aged 57 through 85 years, it was found that 87.1% of them used at least one prescription medication (based on data from “Use of Prescription Over-the-Counter Medications and Dietary SupplementsAmong Older Adultsin the United States,” by Qato et al., Journal of the American Medical Association,Vol. 300,No. 24). Use a 0.01 significance level to test the claim that more than 3/4 of adults use at least one prescription medication. Does the rate of prescription use among adults appear to be high?
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.
Estimates and Hypothesis Tests Data Set 3 “Body Temperatures” in Appendix B includes sample body temperatures. We could use methods of Chapter 7 for making an estimate, or we could use those values to test the common belief that the mean body temperature is 98.6°F. What is the difference between estimating and hypothesis testing?
In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Number and Proportion
a. Identify the actual number of respondents who answered “yes.”
b. Identify the sample proportion and the symbol used to represent it.
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