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Chapter 8: Q. 16 (page 392)

Explain why theP- value of a hypothesis test is also referred to as the observed significance level.

Short Answer

Expert verified

Depending upon the P-value, we can determine whether we can reject or fail to reject our null hypothesis. This is why theP-value of a hypothesis test is also referred to as the observed significance level.

Step by step solution

01

Step 1. Given information

We need to explain why the P-value of a hypothesis test is also referred to as the observed significance level.

02

Step 2. Explanation for the answer:

  • If we rejected our null hypothesis H0,then the P-value must be lesser than or equal to the level of significance.
  • If we failed to reject our null hypothesis H0, the the P-value must be greater than the level of significance.

Therefore, the P-value of the hypothesis test is also referred to as the observed significance level.

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Most popular questions from this chapter

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.

Course Evaluations Data Set 17 鈥淐ourse Evaluations鈥� in Appendix B includes data from student evaluations of courses. The summary statistics are n = 93, x = 3.91, s = 0.53. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00.

Testing Claims About Proportions. In Exercises 9鈥�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.

Cell Phones and Cancer In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today). Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different from the rate of 0.0340% for people who do not use cell phones. Because this issue has such great importance, use a 0.005 significance level. Based on these results, should cell phone users be concerned about cancer of the brain or nervous system?

Identifying H0and H1. In Exercises 5鈥�8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Pulse Rates Claim: The standard deviation of pulse rates of adult males is more than 11 bpm. For the random sample of 153 adult males in Data Set 1 鈥淏ody Data鈥� in Appendix B, the pulse rates have a standard deviation of 11.3 bpm.

Final Conclusions. In Exercises 25鈥�28, use a significance level of = 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: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.

Testing Claims About Proportions. In Exercises 9鈥�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.

Eliquis The drug Eliquis (apixaban) is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed the adverse reaction of nausea (based on data from Bristol-Myers Squibb Co.). Use a 0.05 significance level to test the claim that 3% of Eliquis users develop nausea. Does nausea appear to be a problematic adverse reaction?
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