Testing the Difference Between Two Means In Exercises 9–20, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) calculate
14. Therapeutic Taping A physical therapist claims that the use of a specific type of therapeutic tape reduces pain in patients with chronic tennis elbow. The table shows the pain levels on a scale of 0 to 10, where 0 is no pain and 10 is the worst pain possible, for 15 patients with chronic tennis elbow when holding a 1 kilogram weight. At α = 0.05, is there enough evidence to support the therapist’s claim? (Adapted from BioMed Central, Ltd.)
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Elementary Statistics: Picturing the World (7th Edition)
- Test the claim that the proportion of people who own cats is larger than 20% at the 0.005 significance level. The null and alternative hypothesis would be: H2:p = 0.2 Họ:p 2 0.2 H9:p 0.2 H9:p = 0.2 Hg: u 0.2 H1: u 0.2 The test is: left-tailed two-tailed right-tailed Based on a sample of 300 people, 24% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesisarrow_forwardHypothesis testing will consist of four hypothesis tests which you need to complete. While you will not need to show your work or upload any files, each test will require the following: Type of Test: Null Hypothesis: Alternate Hypothesis: SE: Test Statistic: P-value: Decision: Sentence:arrow_forwardWork Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 29, 50, 41, 29, 24. Use a 0.10 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is. (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) State the conclusion. Ho- There sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes to be equally likely, so the loaded die to behave differently from a fair die.arrow_forward
- Data set presents a sample of the number of defective flash drives produced by a small manufacturing company over the last 30 weeks. The company's operations manager believes that the number of defects produced by the process is less than seven defective flash drives per week. Construct a hypothesis test to verify the operations manager's claim. Hypothesis test should include a t test statistic value, a p value, a decision, and a conclusion. This is the null hypotheses (see attachment): Data: Mean 7.0300 SD 1.3700 SEM 0.2501 N 30arrow_forwardA standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow. Student Math Writing 1 540 474 2 432 380 3 528 463 4 574 612 5 448 420 6 502 526 7 480 424 8 499 459 9 610 615 10 572 541 11 390 329 12 593 613 (a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.) Formulate the hypotheses. 1. H0: μd > 0 Ha: μd ≤ 0 2. H0: μd ≤ 0 Ha: μd = 0 3. H0: μd ≠ 0 Ha: μd = 0 4. H0: μd = 0 Ha: μd ≠ 0 5. H0: μd ≤ 0 Ha: μd > 0 Calculate the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? 1.Do not reject H0. We cannot conclude that there is a significant difference…arrow_forwardA standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow. Student Math Writing 1 540 474 2 432 380 3 528 457 4 574 606 5 448 420 6 502 526 7 480 430 8 499 459 9 610 615 10 572 541 11 390 335 12 593 613 (a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.) Formulate the hypotheses. a) H0: ?d = 0 Ha: ?d ≠ 0 b) H0: ?d ≤ 0 Ha: ?d > 0 c)H0: ?d ≤ 0 Ha: ?d = 0 d) H0: ?d > 0 Ha: ?d ≤ 0 e) H0: ?d ≠ 0 Ha: ?d = 0 Calculate the test statistic. (Round your answer to three decimal places.) answer: _____ Calculate the p-value. (Round your answer to four decimal places.) p-value = answer: ______ What is your conclusion? a) Do not reject H0. We can conclude that there is a significant difference…arrow_forward
- Passive and Active Smoke Data Set 12 “Passive and Active Smoke” in Appendix B lists measured cotinine levels from a sample of subjects who smoke, another sample of subjects who do not smoke but are exposed to environmental tobacco smoke, and a third sample of subjects who do not smoke and are not exposed to environmental tobacco smoke. Cotinine is produced when the body absorbs nicotine. Use a 0.01 significance level to test the claim that the three samples are from populations with the same median. What do the results suggest about a smoker who argues that he absorbs as much nicotine as people who don’t smoke?arrow_forwardHypothesis testing is a systematic procedure for determining whether the results of an experiment are significant. List the 5 steps of hypothesis testing:1.2.3.4.5.arrow_forwardTest the claim that the mean GPA of night students is larger than 3.1 at the 0.01 significance level. The null and alternative hypothesis would be: Но: р — 0.775 Но:р> 0.775 Но: и — 3.1 Но:р 3.1 Н:р+ 0.775 Hi:р 3.1 H]:p > 0.775 Hi:р < 3.1 The test is: right-tailed two-tailed left-tailed Based on a sample of 80 people, the sample mean GPA was 3.14 with a standard deviation of 0.07 The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesisarrow_forward
- Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .025 significance level. The null and alternative hypothesis would be: Ho MMF Ho: PM = PF H₁: MMF O H₁: PM > PF O The test is: two-tailed right-tailed O The test statistic is: Based on a sample of 60 men, 25% owned cats Based on a sample of 40 women, 40% owned cats The p-value is: Ho: M = μF H₁: UMarrow_forwardHypothesis testing is a statistical method that uses data to evaluate a hypothesis about a population (Gravetter, Wallnau & Forzano, 2018). Outline the four steps that allow us to use sample data to answer questions about an unknown population and include your own examples following each step.arrow_forwardHypothesis testing will consist of four hypothesis tests which you need to complete. While you will not need to show your work or upload any files, each test will require the following: Type of Test: Null Hypothesis: Alternate Hypothesis: SE: Test Statistic: P-value: Decision: Sentence:arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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