Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms (“Gastrointestinal Symptoms Following Consumption of Olestra or Regular Triglyceride Potato Chips,” J. of the Amer. Med. Assoc., 1998: 150–152). Among 529 individuals in the TG control group, 17.6% experienced an adverse GI
a. Carry out a test of hypotheses at the 5% significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment.
b. If the true percentages for the two treatments were 15% and 20%, respectively, what
Trending nowThis is a popular solution!
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
- A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.arrow_forwardDoes It Pay to Plead Guilty? The accompanying table summarizes randomly selected sample data for San Francisco defendants in burglary cases (based on data from “Does It Pay to Plead Guilty? Differential Sentencing and the Functioning of the Criminal Courts,” by Brereton and Casper, Law and Society Review, Vol. 16, No. 1). All of the subjects had prior prison sentences. Use a 0.05 significance level to test the claim that the sentence (sent to prison or not sent to prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?arrow_forwardAn article from the American Journal of Public Health reports the results from a randomized study designed to evaluate the efficacy of an intervention targeted to Hispanic/Latino men who identify as gay, bi-sexual or other men who have sex with men (MSM). A representative sample of 254 such men was randomized to be in either the intervention group (n=152, with 141 ultimately participating in the study) or the control group (n=152, with 147 ulitmately participating in the study). The primary outcome under study getting tested for HIV within the six-months following group assignment (randomization) among those who had been sexually active in this same six-month follow-up period. At six months of follow-up, 141 subjects in the intervention group reported having had sex (with men and/or women) since randomization. Of these 141 men, 114 had been tested for HIV since being randomized. At six months of follow-up, 147 subjects in the control group reported having had sex (with men…arrow_forward
- A case–control study of patients on antihypertensive drugs related an increased risk of myocardial infarction (MI) for patients using calcium channel blockers (Psaty, et al.,1995). In this study, cases were antihypertensive drug patients who had suffered a first fatal or nonfatal MI through 1993, and controls were antihypertensive patients, matched by demographic factors, who had not suffered a MI. Among the comparisons reported were patients receiving calcium channel (CC) blockers (with and without diuretics) and patients receiving β–blockers (with and without diuretics). Results of numbers of patient by drug/MI status combination are given in Table 1. Compute the odds ratio of suffering MI (CC blockers relative to β–blockers), and the corresponding 95% CI. Does it appear that calcium channel blockers are associated with higher odds (and thus probability) of suffering MI than β –blockers? Table 1: Observed cell counts for antihypertensive drug/MI data Occurrence of…arrow_forwardA standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum Mean 75.31914894 65.65957447 Variance 118.613321 801.1424607 Observations 47 47 Pooled Variance 459.8778908 Hypothesized Mean Difference 0 df 92 t Stat 2.1835887807 P(T<=)one tail 0.015768226 t Critical one-tail 1.661585397 P(T<=t) two-tail 0.031536452 t Critical two-tail 1.986086317 You decide to use the conventional p=.05 as your cutoff for statistical significance. What do you conclude from this analysis? a.…arrow_forwardRogers, Farlow, and colleagues (1998) conducted an experiment to investigate whether donepezil improved cognitive function in patients with mild to moderate Alzheimer’s disease (AD). A total of 1,775 patients were randomly assigned to treatment with either donepezil or a placebo (a look-alike pill with no pharmacological effect). Cognitive function, as measured by the Alzheimer’s Disease Assessment Scale (ADAS-cog), was significantly improved in patients taking donepezil compared with the placebo group at weeks 12, 18, and 24. [Source: Rogers, S. L., Farlow, M. R., Doody, R. S., et al. (1998). A 24-week, double-blind, placebo controlled trial of donepezil in patients with Alzheimer’s disease. Neurology, 50, 136–145.] In this experiment, the independent variable is , and the dependent variable is . The individuals who are in the control condition are typically referred to as the control group. Here, the control group consists of . is a construct that is being tested in this…arrow_forward
- A 2017 article in The New England Journal of Medicine details the results of a randomized clinical trial designed to evaluate the efficacy of a rotavirus gastroenteritis vaccine designed for infants. As per the authors: “Each year, rotavirus gastroenteritis is responsible for about 37% of deaths from diarrhea among children younger than 5 years of age worldwide, with a disproportionate effect in sub-Saharan Africa. We conducted a randomized, placebo-controlled trial in Niger to evaluate the efficacy of a live, oral bovine rotavirus pentavalent vaccine (BRV-PV, Serum Institute of India) to prevent severe rotavirus gastroenteritis. Healthy infants received three doses of the vaccine or placebo at 6, 10, and 14 weeks of age. Episodes of rotavirus gastroenteritis were assessed through active and passive surveillance.” The following Kaplan-Meier curves show the time to a diagnosis of rotavirus gastroenteritis separately for the vaccine and placebo samples. Infants were followed for up to 60…arrow_forwardIn a recent study of a random sample of 113 people, 92 reported dreaming in color. In the 1940’s, the proportion of people who reported dreaming in color was 29%. Is there evidence to show that the proportion of people who dream in color is different than the proportion in the 1940’s? What is the decision for this hypothesis test? A) Fail to reject Ho because the test statistic is in the rejection region and the p-value is greater than alpha. B)Fail to reject Ho because the test statistic is not in the rejection region and the p-value is greater than alpha. C) Reject Ho because the test statistic is in the critical region and the p-value is less than alpha. D) Fail to reject Ho because the test statistic is in the critical region and the p-value is less than alpha. E) Reject Ho because the test statistic is in the rejection region and the p-value is greater than alpha.arrow_forwardThe article “Capillary Leak Syndrome in Children with C4A-Deficiency Undergoing Cardiac Surgery with Cardiopulmonary Bypass: A Double-Blind, Randomised Controlled Study” (S. Zhang, S. Wang, et al., Lancet, 2005:556–562) presents the results of a study of the effectiveness of giving blood plasma containing complement component C4A to pediatric cardiopulmonary bypass patients. Of 58 patients receiving C4A-rich plasma, the average length of hospital stay was 8.5 days and the standard deviation was 1.9 days. Of 58 patients receiving C4A-free plasma, the average length of hospital stay was 11.9 days and the standard deviation was 3.6 days. Can you conclude that the mean hospital stay is shorter for patients receiving C4A-rich plasma?arrow_forward
- The dry shear strength of birch plywood bonded with different resin glues was studied with a completely randomized designed experiment. Here are the data: Glue A (102; 58; 45; 79; 68; 63; 117) Glue C (100; 102; 80; 119) Glue F (220; 243; 189; 176; 176). SSE = 8167.55; MSE = 628.27; and F stat = 37.99. What is the critical value at the 5% significance level (rounded off 2 decimals)?arrow_forwardIndependent random samples of 32 people living on the west side of a city and 30 people living on the east side of a city were taken to determine if the income levels of west side residents are significantly different from the income levels of east side residents. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the income levels of west side residents are significantly different from the income levels of east side residents, at the 2% significance level. H0:μw=μeHa:μw≠μe t0=2.364 t0.01=±2.099 Select the correct answer below: No; the test statistic is not between the critical values. No; the test statistic is between the critical values. Yes; the test statistic is not between the critical values. Yes; the test statistic is between the critical values.arrow_forwardA standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: t-test: Two-Sample Assuming Equal Variances Old Curriculum New Curriculum Mean 75.31914894 65.65957447 Variance 118.613321 801.1424607 Obervations 47 47 Hypothesized Mean Difference 0 df 92 t Stat 2.183587807 P(T<=t) one-tail 0.015768226 t Critical one-tail 1.661585397 P(T<=t) two-tail 0.031536452 t Critical two-tail…arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman