Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. The article “Efficacy of the Addition of Modified Pilates Exercises to a Minimal Intervention in Patients with Chronic Low Back Pain: A Randomized Controlled Trial” (Physical Therapy, 2013: 309–321) reported on an experiment involving 86 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample
a. Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of .01 (the cited article reported statistical significance at this a, and a sample mean difference of 2.1 also suggests practical significance).
b. Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1? Carry out a test of appropriate hypotheses.
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Chapter 9 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- Female college student participation in athletics has increased dramatically over the past few decades. Sports medicine providers are aware of some unique health concerns of athletic women, including disordered eating. A study compared disordered-eating symptoms and their causes for collegiate female athletes (in lean and non lean sports) and nonathletes. The sample mean of the body dissatisfaction assessment score was 13.4 (s=7.9) for 15 lean sports athletes (those sports that place value on leanness, including distance running, swimming, and gymnastics) and 7.4 (s=5.8) for the 67 non-lean athletes. Assume equal population standard deviations. Find the standard error for comparing the means. Construct a 95% confidence interval for the difference between the mean body dissatisfaction for lean sport athletes and non lean sport athletes. Interpret.arrow_forwardCash flow and profits are both crucial aspects of a business. Profit is the surplus revenue after deducting business expenses. Cash flow is the total amount of cash moving in and out of your business. For a business to be successful in the long term, it needs to generate profits while also operating with positive cash flow. During the Covid-19 pandemic, however, of a random sample of 199 auditors, 104 indicated some measure of agreement with this statement: cash flow is more important to keep the business operating on a day-to-day basis. a) Investigate the claim that one-half of the members of this population would agree with this statement. Also, find and interpret the p-value of this test. b) Find the probability of accepting the claim with a 10%-level test if, in fact, 60% of all auditors agree that cash flow is an important indicator to keep the business operating on a day-to-day basis.arrow_forwardAre seatbelts effective at saving lives? We wish to examine whether or not the use of seatbelts reduces fatalities at the a = 0.01 level of significance. Let pN represent the proportion of non-seatbelt wearing passengers who were involved in a crash and died and py represent the proportion of seatbelt wearing passengers who were involved in a crash and died. NOTE: The data used in this study were obtained through observational study...no experiment was conducted! Which would be correct hypotheses for this test? O Ho:PN = pY, H1:PN > pY Ho: PN = pY, H,:PN Py In a random sample of 321 non-seatbelt wearing passengers involved in a car crash, 30 were killed. In a random sample of 492 seatbelt wearing passengers involved in a car crash, 13 were killed. Find the test statistic (2 decimal places): Give the P-value (4 decimal places - if less than 0.001 answer 0): Which is the correct result: Reject the Null Hypothesis O Do not Reject the Null Hypothesis Which would be the appropriate…arrow_forward
- Researchers have sought to examine the effect of various types of music on agitation levels in patients who are in the early and middle stages of Alzheimer's disease. Patients were selected to participate in the study based on their stage of Alzheimer's disease. Three forms of music were tested: Easy listening, Mozart, and piano interludes. While listening to music, agitation levels were recorded for the patients with a high score indicating a higher level of agitation. Scores are recorded below. Group Piano Interlude Mozart Easy Listening Early Stage Alzheimer's 2124221820 Mean=21.0 9121059 Mean=9.0 2926302426 Mean=27.0 Middle Stage Alzheimer's 2220251820 Mean=21.0 141811913 Mean=13.0 1518201319 Mean=17.0 Complete the following ANOVA table. Source df SS MS F Type of Music 2 740 Degree of Alzheimer's 1 30 Interaction 2 260 Error 24 178 Total 29 1208…arrow_forward(True or False) A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants are enrolled in the study and randomized to receive either the experimental medication or placebo. The primary outcome is self-reported reduction of symptoms. Among 50 participants who receive the experimental medication, 30 report a reduction of symptoms as compared to 15 participants of 50 assigned to the placebo. The 95% CI for the relative risk of participants reporting a reduction of symptoms between the experimental and placebo groups is between 1.529 and 8.012.arrow_forwardResearchers studying the effect of antibiotic treatment compared to symptomatic treatment for acute sinusitis randomly assigned 166 adults diagnosed with sinusitis into two groups. Participants in the antibiotic group received a 10-day course of an antibiotic, and the rest received symptomatic treatments as a placebo. These pills had the same taste and packaging as the antibiotic. At the end of the 10-day period patients were asked if they experienced improvement in symptoms since the beginning of the study. The distribution of responses is summarized below. Antibiotic Placebo Total Yes 72 60 132 No 13 21 31 Total 85 81 166 A simulation was conducted under the assumpton that the proportion of self-reported improvement with the antibiotic treatment is equal to the proportion of self-reported improvement with the palcebo. 100,000 simulated differences were generated to construct the null distribution shown. The value ˆpa,∼p^a,∼ represents the proportion of self-reported…arrow_forward
- In this study, ten combat veterans undergoing treatment for PTSD were randomly sampled from a local VA hospital in a study designed to test the efficacy of an anti-anxiety medication in reducing the symptoms of PTSD. Based on clinical animal trials, the researchers predict that the drug should reduce symptoms. t= 1.63, df=9, p=0.064, d= 0.529. Before: M= 48.100, SD=1.370, SE=0.433 After: M= 47.000, SD= 1.491, SE= 0.471 My hypotheses are; H0: μbefore ≤ μafter. H1: μbefore > μafter A. State your findings in APA format: B. How would you explain these findings to someone who has never taken a statistics class? In other words, use clear direct, non-jargon language to explain the results:arrow_forwardStressed-Out Bus Drivers. Previous studies have shown that urban bus drivers have an extremely stressful job, and a large proportion of drivers retire prematurely with disabilities due to occupational stress. In the paper, “Hassles on the Job: A Study of a Job Intervention With Urban Bus Drivers” (Journal of Organizational Behavior, Vol. 20, pp. 199–208), G. Evans et al. examined the effects of an intervention program to improve the conditions of urban bus drivers.Amongother variables, the researchers monitored diastolic blood pressure of bus drivers in downtown Stockholm, Sweden. The data, in millimeters of mercury (mm Hg), on the WeissStats site are based on the blood pressures obtained prior to intervention for the 41 bus drivers in the study. Use the technology of your choice to do the following. a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data. b. Based on your results from part (a), can you reasonably apply the one-mean t-test to the…arrow_forwardThe authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement" compared two different instruments for measuring a subject's ability to breathe out air.+ (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen subjects participated in the study, and for each subject air flow was measured once using the Wright meter and once using the mini-Wright meter. Mini- Subject Wright Meter 1 2 3 4 5 6 7 8 9 512 430 520 428 500 600 364 380 658 Wright Meter 494 395 516 434 476 557 413 442 650 Subject 10 11 12 13 14 15 16 17 Mini- Wright Meter 445 432 626 260 477 259 350 451 Wright Meter 433 417 656 267 478 178 423 427 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different readings but there is a…arrow_forward
- In a clinical trial of 2029 subjects treated with a certain drug, 22 reported headaches. In a control group of 1572 subjects given a placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by pt and denoting the proportion of headaches in the control (placebo) group by pc, the relative risk is pt/pc. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating StartFraction p Subscript t Baseline divided by left parenthesis 1 minus p Subscript t Baseline right parenthesis Over p Subscript c Baseline divided by left parenthesis 1 minus p Subscript c Baseline right parenthesis EndFractionpt/1−ptpc/1−pc. The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and…arrow_forwardResearchers studying the effect of antibiotic treatment for acute sinusitis compared to symptomatic treatments randomly assigned 166 adults diagnosed with acute sinusitis to one of two groups: treatment or control. Study participants received either a 10-day course of amoxicillin (an antibiotic) or a placebo similar in appearance and taste. The placebo consisted of symptoatic treatments such as acetaminophen, nasal decongestants, etc. At the end of the 10-day period, patients were asked if they experienced improvement in symptoms. The distribution of responses is summized below. We want to test if there is a difference in the improvement rates of sinusitis symptoms between the treatment and the placebo.(a) Formulate the null and alternative hypotheses(b) Calculate the test statistic and find the P-value(c) Please check the conditions required to do the test above.arrow_forwardA clinician was interested in exploring functionality in patients following a stroke rehabilitation program. Participants were recruited through the rehabilitation unit at Providence Care Hospital. Functional status was evaluated at baseline (immediately following stroke), and 8 weeks later. Patients’ functional outcomes were rated on the following 5-point scale: 1 – poor, 2- fair, 3 – moderate, 4 -good, 5 – excellent. The clinician wants to know whether patients improved their functioning over the 8-week period. 1. Under the heading “Results” present your findings (i.e., what you found).Include at least one measure of central tendency and variability. An assumption check(describe what you did and what you found, as needed), check for potential outliers,and present the findings of your inferential test (i.e., your critical value and p value), asappropriate. Patient Baseline Functional Status (1 to 5) 8 week follow up functional status (1 to 5) 1 4 3 2 1 2 3 3 3 4 5 4 5 4 1…arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt