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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MYLAB STATISTICS: ELEMENTARY STATISTICS
- (c) Calculate the test statistic. d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.arrow_forward(c) Calculate the test statistic. d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.arrow_forwardTest the claim that the mean GPA of Orange Coast students is larger than the mean GPA of Coastline students at the 0.01 significance level. The null and alternative hypothesis would be: Ho:μο = μc Ho:μο με H1:po pc Hy:μο < με Reject the null hypothesis O Fail to reject the null hypothesis (to 2 decimals) (to 2 decimals)arrow_forward
- Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.05 significance level. The null and alternative hypothesis would be: Ho:PN 2 PD Ho:PN = PD Ho: PN PD H1:UN > HD H1:uN Next Question M hparrow_forwardTest the claim that the mean GPA of Orange Coast students is smaller than the mean GPA of Coastline students at the 0.01 significance level. The null and alternative hypothesis would be: Ho:Po = Pc Ho:Po > Pc Ho:µ0 µc H1: Ho Pc H1:µo + HC The test is: two-tailed left-tailed right-tailed The sample consisted of 55 Orange Coast students, with a sample mean GPA of 3.46 and a standard deviation of 0.08, and 55 Coastline students, with a sample mean GPA of 3.49 and 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 Fail to reject the null hypothesis Reject the null hypothesisarrow_forwardTest 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_forward
- A hypothesis test result is considered to be statistically significant only when?arrow_forwardIllustrate the null hypothesis for a correlated t test?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
- Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.05 significance level. The null and alternative hypothesis would be: Ho: PNPD Ho: UN ≤ HD Ha:N HD Ha:μN > HD The test is: right-tailed two-tailed left-tailed O Ho: PNPD Ho: PNPD Ho: PN Ha:PN PD Oarrow_forwardExplain the three types of t-tests (one-sample, two-sample independent and two-sample dependent t test) and include an example of each. What are the assumptions for using a two-sample independent t test?arrow_forwardTest the claim that the proportion of people who own cats is smaller than 80% at the 0.10 significance level. The null and alternative hypothesis would be: 0.8 Но: д — 0.8 Но:д 0.8 Но:р > 0.8 Нo:р H1: µ 0.8 H1:p > 0.8 The test is: left-tailed right-tailed two-tailed Based on a sample of 800 people, 73% owned cats The p-value is: (to 2 decimals) Based on this we: O Reject the null hypothesis Fail to reject the null hypothesisarrow_forward
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