Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 12.4, Problem 46E
Astringency is the quality in a wine that makes the wine drinker’s mouth feel slightly rough, dry, and puckery. The paper “Analysis of Tannins in Red Wine Using
| x | .718 | .808 | .924 1.000 | .667 | .529 | .514 | .559 |
| y | .428 | .480 | .493 .978 | .318 | .298 | −.224 | .198 |
| x | .766 | .470 | .726 | .762 | .666 | .562 | .378 | .779 |
| y | .326 | −.336 | .765 | .190 | .066 | −.221 | −.898 | .836 |
| x | .674 | .858 | .406 | .927 | .311 | .319 | .518 | .687 |
| y | .126 | .305 | −.577 | .779 | −.707 | −.610 | −.648 | −.145 |
| x | .907 | .638 | .234 | .781 | .326 | .433 | .319 | .238 |
| y | 1.007 | −.090 | −1.132 | .538 | −1.098 | −.581 | −.862 | -.551 |
Relevant summary quantities are as follows:
- a. Fit the simple linear regression model to this data. Then determine the proportion of observed variation in astringency that can be attributed to the model relationship between astringency and tannin concentration.
- b. Calculate and interpret a confidence interval for the slope of the true regression line.
- c. Estimate true average astringency when tannin concentration is .6, and do so in a way that conveys information about reliability and precision.
- d. Predict astringency for a single wine sample whose tannin concentration is .6, and do so in a way that conveys information about reliability and precision.
- e. Does it appear that true average astringency for a tannin concentration of .7 is something other than 0? State and test the appropriate hypotheses.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Stressed-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…
Low-Birth-Weight Hospital Stays. Data on low-birthweight babies were collected over a 2-year period by 14 participating centers of the National Institute of Child Health and Human Development Neonatal Research Network. Results were reported by J. Lemons et al. in the on-line paper “Very Low Birth Weight Outcomes of the National Institute of ChildHealth and Human Development Neonatal Research Network” (Pediatrics, Vol. 107, No. 1, p. e1). For the 1084 surviving babies whose birth weights were 751– 1000 grams, the average length of stay in the hospital was 86 days, although one center had an average of 66 days and another had an average of 108 days.
a. Can the mean lengths of stay be considered population means? Explain your answer.b. Assuming that the population standard deviation is 12 days, determine the z-score for a baby’s length of stay of 86 days at the center where the mean was 66 days.c. Assuming that the population standard deviation is 12 days, determine the z-score for a…
Pulmonary Hypertension. In the paper “Persistent Pulmonary Hypertension of the Neonate and Asymmetric Growth Restriction” (Obstetrics&Gynecology, Vol. 91, No. 3, pp. 336–341), M. Williams et al. reported on a study of characteristics of neonates. Infants treated for pulmonary hypertension, called the PH group, were compared with those not so treated, called the control group. One of the characteristics measured was head circumference. The mean head circumference of the 10 infants in the PH group was 34.2 centimeters (cm).
a. Assuming that head circumferences for infants treated for pulmonary hypertension are normally distributed with standard deviation 2.1 cm, determine a 90% confidence interval for the mean head circumference of all such infants.
b. Obtain the margin of error, E, for the confidence interval you found in part (a).
c. Explain the meaning of E in this context in terms of the accuracy of the estimate.
d. Determine the sample size required to have a margin of error of…
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 12.1 - The efficiency ratio for a steel specimen immersed...Ch. 12.1 - The article Exhaust Emissions from Four-Stroke...Ch. 12.1 - Bivariate data often arises from the use of two...Ch. 12.1 - The accompanying data on y = ammonium...Ch. 12.1 - The article Objective Measurement of the...Ch. 12.1 - One factor in the development of tennis elbow, a...Ch. 12.1 - The article Some Field Experience in the Use of an...Ch. 12.1 - Referring to Exercise 7, suppose that the standard...Ch. 12.1 - The flow rate y (m3/min) in a device used for...Ch. 12.1 - Suppose the expected cost of a production run is...
Ch. 12.1 - Suppose that in a certain chemical process the...Ch. 12.2 - Refer back to the data in Exercise 4, in which y =...Ch. 12.2 - The accompanying data on y = ammonium...Ch. 12.2 - Refer to the lank temperature-efficiency ratio...Ch. 12.2 - Values of modulus of elasticity (MOE, the ratio of...Ch. 12.2 - The article Characterization of Highway Runoff in...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - The following data is representative of that...Ch. 12.2 - The bond behavior of reinforcing bars is an...Ch. 12.2 - Wrinkle recovery angle and tensile strength are...Ch. 12.2 - Calcium phosphate cement is gaining increasing...Ch. 12.2 - a. Obtain SSE for the data in Exercise 19 from the...Ch. 12.2 - The invasive diatom species Didymosphenia geminata...Ch. 12.2 - Prob. 25ECh. 12.2 - Show that the point of averages (x,y) lies on the...Ch. 12.2 - Prob. 27ECh. 12.2 - a. Consider the data in Exercise 20. Suppose that...Ch. 12.2 - Consider the following three data sets, in which...Ch. 12.3 - Reconsider the situation described in Exercise 7,...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - Exercise 16 of Section 12.2 gave data on x =...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - For the past decade, rubber powder has been used...Ch. 12.3 - Refer back to the data in Exercise 4, in which y =...Ch. 12.3 - Misi (airborne droplets or aerosols) is generated...Ch. 12.3 - Prob. 37ECh. 12.3 - Refer to the data on x = liberation rate and y =...Ch. 12.3 - Carry out the model utility test using the ANOVA...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Verify that if each xi is multiplied by a positive...Ch. 12.3 - Prob. 43ECh. 12.4 - Fitting the simple linear regression model to the...Ch. 12.4 - Reconsider the filtration ratemoisture content...Ch. 12.4 - Astringency is the quality in a wine that makes...Ch. 12.4 - The simple linear regression model provides a very...Ch. 12.4 - Prob. 48ECh. 12.4 - You are told that a 95% CI for expected lead...Ch. 12.4 - Prob. 50ECh. 12.4 - Refer to Example 12.12 in which x = test track...Ch. 12.4 - Plasma etching is essential to the fine-line...Ch. 12.4 - Consider the following four intervals based on the...Ch. 12.4 - The height of a patient is useful for a variety of...Ch. 12.4 - Prob. 55ECh. 12.4 - The article Bone Density and Insertion Torque as...Ch. 12.5 - The article Behavioural Effects of Mobile...Ch. 12.5 - The Turbine Oil Oxidation Test (TOST) and the...Ch. 12.5 - Toughness and fibrousness of asparagus are major...Ch. 12.5 - Head movement evaluations are important because...Ch. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - The accompanying data on x = UV transparency index...Ch. 12.5 - Torsion during hip external rotation and extension...Ch. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12 - The appraisal of a warehouse can appear...Ch. 12 - Prob. 69SECh. 12 - Forensic scientists are often interested in making...Ch. 12 - Phenolic compounds are found in the effluents of...Ch. 12 - The SAS output at the bottom of this page is based...Ch. 12 - The presence of hard alloy carbides in high...Ch. 12 - The accompanying data was read from a scatterplot...Ch. 12 - An investigation was carried out to study the...Ch. 12 - Prob. 76SECh. 12 - Open water oil spills can wreak terrible...Ch. 12 - In Section 12.4, we presented a formula for...Ch. 12 - Show that SSE=Syy1Sxy, which gives an alternative...Ch. 12 - Suppose that x and y are positive variables and...Ch. 12 - Let sx and sy denote the sample standard...Ch. 12 - Verify that the t statistic for testing H0: 1 = 0...Ch. 12 - Use the formula for computing SSE to verify that...Ch. 12 - In biofiltration of wastewater, air discharged...Ch. 12 - Normal hatchery processes in aquaculture...Ch. 12 - Prob. 86SECh. 12 - Prob. 87SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Aortic stenosis refers to a narrowing of the aortic valvein the heart. The article “Correlation Analysis ofStenotic Aortic Valve Flow Patterns Using PhaseContrast MRI” (Annals of Biomed. Engr., 2005:878–887) gave the following data on aortic root diameter(cm) and gender for a sample of patients having variousdegrees of aortic stenosis:M: 3.7 3.4 3.7 4.0 3.9 3.8 3.4 3.6 3.1 4.0 3.4 3.8 3.5F: 3.8 2.6 3.2 3.0 4.3 3.5 3.1 3.1 3.2 3.0a. Compare and contrast the diameter observations forthe two genders.b. Calculate a 10% trimmed mean for each of the twosamples, and compare to other measures of center(for the male sample, the interpolation method mentionedin Section 1.3 must be used).arrow_forwardDexamethasone and IQ. In the paper “Outcomes at School Age After Postnatal Dexamethasone Therapy for Lung Disease of Prematurity” (New England Journal of Medicine, Vol. 350, No. 13, pp. 1304–1313), T. Yeh et al. studied the outcomes at school age in children who had participated in a double-blind, placebo-controlled trial of early postnatal dexamethasone therapy for the prevention of chronic lung disease of prematurity. All of the infants in the study had had severe respiratory distress syndrome requiring mechanical ventilation shortly after birth. On the WeissStats site, we provide the school-age IQs of the 74 children in the control group, based on the study results. 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 one-standard-deviation χ2-procedures to the data? Explain your reasoning. c. Overall, IQs of school-age…arrow_forwardA Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. What conclusion can you draw from the output? The data provide sufficient evidence to reject H0 and to conclude that the mean depression score for male teens is larger than that of female teens. The data provide sufficient evidence to conclude that male and female teens do not differ in mean depression score. The data do not provide sufficient evidence to conclude that the mean depression score of male teens is larger than that of female teens. The data do not provide sufficient evidence to reject H0, so we accept it, and conclude that male and female teens do…arrow_forward
- Is Seat Belt Use Independent of Cigarette Smoking?A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and Comstock,American Journal of Public Health,Vol. 67, No. 11). Test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?arrow_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_forwardLactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004: 1322–1326) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P). SubjectL 1928 2549 2825 1924 1628 2175 2114 2621 1843 2541P 2126 2885 2895 1942 1750 2184 2164 2626 2006 2627 Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of .05.arrow_forward
- A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. If μ1 and μ2 represent the mean depression score for male teens and female teens respectively, which of the following is an appropriate pair of hypotheses in this case? Check all that apply.arrow_forwardA study was conducted to assess the association between certain pollutants/behaviors and respiratory function. The response measured was chronic respiratory disease status where subjects were assigned to one of four possible categories (Level 1 = no symptoms, Level 2 = cough or phlegm ≤ 3 months per year, Level 3 = cough or phlegm > 3 months per year, Level 4 = cough or phlegm and shortness of breath > 3 months per year). The explanatory variables of interest are Air Pollution (air = low, high), Job Exposure to Pollution (exposure = no, yes), and Smoking Status (smoking = non, ex, current). The SAS data step for this data set is given below: Construct a proportional odds model using level as the response variable. Select only the appropriate predictors in the final model. After the final model is constructed, compare each level of response against the level 1 symptom group. Based on the final model, write a report about your findings – include hypotheses,…arrow_forwardThe article “Dynamics of Insulin Action in Hypertension: Assessment from Minimal ModelInterpretation of Intravenous Glucose Tolerance Test Data” (R. Burattini, M. Morettini, etal., Med Biol Eng Comput, 2011:831–841) compared levels of an insulin sensitivity index SIin patients with high blood pressure and patients with normal blood pressure. Ten patientswith high blood pressure had a mean value of 3.4 with a standard deviation of 0.6, and eightpatients with normal blood pressure had a mean value of 7.9 with a standard deviation of0.6. Units are 10−5 · min−1 · pmol−1. Find a 98% confidence interval for the difference inmean levels between those with high blood pressure and those with normal blood pressure.arrow_forward
- An article23 summarized results from the Nurses’ Health Study and the Health Pro- fessionals Follow-Up Study. The article reported (with RR = relative risk) that “Com- pared with nonregular use, regular aspirin use was associated with lower risk of overall cancer (RR 0.97; 95% CI 0.94, 0.99), which was primarily due to a lower incidence of gastrointestinal cancers, especially colorectal cancers (RR 0.81; 95% CI 0.75, 0.88).” Identify the response variables and the explanatory variable for these two results. Explain how to interpret the confidence interval about colorectal cancers. Would the association with overall cancer be considered (i) significant or non- significant? (ii) strong or weak? Explain. question 1 and 2arrow_forwardA fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 d-Test the…arrow_forwardIs Echinacea Effective for Colds? Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 40 of the 45 subjects treated with echinacea developed rhi-novirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). We want to use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, does echinacea appear to have any effect on the infection rate?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics 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:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License