The paper “Mood Food: Chocolate and Depressive Symptoms in a Cross-Sectional Analysis” (Archives of Internal Medicine [2010]: 699–703) describes a study that investigated the relationship between depression and chocolate consumption. Participants in the study were 931 adults who were not currently taking medication for depression. These participants were screened for depression using a widely used screening test. The participants were then divided into two samples based on the score on the screening test. One sample consisted of people who screened positive for depression, and the other sample consisted of people who did not screen positive for depression. Each of the study participants also completed a food frequency survey.
The researchers believed that the two samples were representative of the two populations of interest—adults who would screen positive for depression and adults who would not screen positive. The paper reported that the
Estimate the difference in the mean number of servings of chocolate per month in the population of people who would screen positive for depression and the mean number of chocolate servings per month in the population of people who would not screen positive for depression. Use a confidence level of 90% and be sure to interpret the interval in context.
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Chapter 11 Solutions
INTRODUCTION TO STATISTICS & DATA ANALYS
- In a study of three nationally representative large- scale data sets from Ireland, the United States, and the United Kingdom (n = 17,247), teenagers between the ages of 12 to 15 were asked to keep a diary of their screen time and answer questions about how they felt or acted. Identify the explanatory variables. Comment on wheter the results of the study can be generalized to the population and whyarrow_forwardA consumer advocacy group wanted to study whether different airline carriers differed in terms of their delayed flights. In particular, the researchers were interested in the relationship between p1, the proportion of Alpha Airlines flights that were delayed at least 15 minutes, and p2, the proportion of Beta Airlines flights that were delayed at least 15 minutes. A random sample of 1,000 Alpha flights and a separate random sample of 1,000 Beta flights found that 67 of the Alpha fights and 160 of the Beta flights were delayed at least 15 minutes. The conditions for inference were checked and verified. Does this set of samples provide strong evidence that Alpha Airlines has a smaller proportion of flights that are delayed at least 15 minutes than Beta Airlines, at the α = 0.05 significance level? Find the z-table here. A. The test statistic is z = –6.56 and the P-value ≈ 0. Since the P-value ≈ 0 < 0.05, there is not sufficient evidence that Alpha Airlines has fewer delayed…arrow_forwardThe article “Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease With and Without Intermittent Claudication. A Randomized Controlled Trial” (M. McDermott, P. Ades, et al., Journal of the American Medical Association, 2009:165–174) reported the results of a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 48 patients walked on a treadmill for six minutes every day. After six months, the mean distance walked in six minutes was 348 m, with a standard deviation of 80 m. For a control group of 46 patients who did not walk on a treadmill, the mean distance was 309 m with a standard deviation of 89 m. Find a 95% confidence interval for the difference in mean distance walked between the two groups of patients.arrow_forward
- The article “Treadmill Exercise and Resistance Training in Patients With Peripheral Arterial Disease With and Without Intermittent Claudication. A Randomized Controlled Trial” (M. McDermott, P. Ades, et al., Journal of the American Medical Association, 2009:165–174) reported the results of a study to determine whether treadmill exercise could improve the walking ability of patients suffering from claudication, which is pain caused by insufficient blood flow to the muscles of the legs. A sample of 48 patients walked on a treadmill for six minutes every day. After six months, the mean distance walked in six minutes was 348 meters, with a standard deviation of 80 m. For a control group of 46 patients who did not walk on a treadmill, the mean distance was 309 m with a standard deviation of 89 m. Can you conclude that the mean distance walked for patients using a treadmill is greater than the mean for the controls? Use the α = 0.05 level of significance.arrow_forwardThree experiments investigating the relation between need for cognitive closure and persuasion were reported in “Motivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information,” by A. W. Kruglanski (Journal of Personality and Social Psychology, Vol. 65, No. 5, pp. 861–874). Part of the study involved administering a “need for closure scale” to a group of students enrolled in an introductory psychology course. The “need for closure scale” has scores ranging from 101 to 201. For the 73 students in the highest quartile of the distribution, the mean score was 178.70 . Assume a population standard deviation of 7.81. These students were all classified as high on their need for closure. Assume that the 73 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score on the “need for closure scale” for all students with a high need for closurearrow_forwardA 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_forward
- A study was performed on 200 elementary school students to investigate whether regular Vitamin A supplementation was effective in preventing colds during the month of March. 100 were randomized to receive daily Vitamin A supplements during the month of March, and 100 students were randomized to a placebo group (and did not receive Vitamin A) during the same month. The number of students getting at least one cold in March was computed in the two groups, and the results are given in the following 2 X 2 table. Using a 5% level of significance determine whether there is an association between Vitamin A supplementation and prevention of Common Cold ColdNo Cold Vitamin A1585100 Placebo2575100 40160200arrow_forwardAspirin and Cardiovascular Disease. In the article by P. Ridker et al. titled “A Randomized Trial of Low-dose Aspirin in the Primary Prevention of Cardiovascular Disease inWomen” (New England Journal of Medicine, Vol. 352, pp. 1293–1304), the researchers noted that “We randomly assigned 39,876 initially healthy women 45 years of age or older to receive 100 mg of aspirin or placebo on alternate days and then monitored them for 10 years for a first major cardiovascular event (i.e., nonfatal myocardial infarction, nonfatal stroke, or death from cardiovascular causes).”arrow_forwardIn their study of the effectiveness of cardiac catheterization, McClellan,McNeil, and Newhouse (1994) used as an instrument the difference indistance to cardiac catheterization and regular hospitals. How could youdetermine whether this instrument is relevant? How could you determinewhether this instrument is exogenous?arrow_forward
- Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy (periconceptional period). (Schmidt, 2011) Autism Typical Development Total No vitamin 111 70 181 Vitamin 143 159 302 Total 254 229 483 Complete the hypothesis test and state an appropriate conclusion.What is the value of the test statistic for this test? (Please round to two decimal places) What is the p-value associated with this test? (Please round to four decimal places)arrow_forwardA low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. (10)b) A CDC press release publishing the results of this study claims that…arrow_forwardA low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. b) A CDC press release publishing the results of this study claims that…arrow_forward
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