Concept explainers
Phyllodes Tumors. Phyllodes tumors of the breast are rare tumors that represent less than one percent of growths in the breast. Researchers I. Youn et al. presented characteristics of phyllodes tumors in the article “Phyllodes Tumors of the Breast: Ultrasonographic Findings and Diagnostic Performance of Ultrasound-Guided Core Needle Biopsy” (Ultrasound in Medicine and Biology, Vol. 39, No. 6, pp. 987–992). The following table provides summary statistics for the sizes, in millimeters (mm), of independent samples of benign and malignant phyllodes tumors.
Malignant | Benign |
|
|
s1 = 38.5 | s2 = 26.6 |
n1 = 52 | n2 = 116 |
At the 1% significance level, do the data provide sufficient evidence to conclude that, on average, malignant phyllodes tumors are larger than benign phyllodes tumors?
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Introductory Statistics (10th Edition)
- Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities?arrow_forwardBefore/After Treatment Results Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme,” by MacGregor et al., British Medical Journal, Vol. 2). Using a 0.01 significance level, is there sufficient evidence to support the claim that Captopril is effective in lowering systolic blood pressure?arrow_forwardPostponing Death An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study, it was found that there were 6062 deaths in the week before Thanksgiving, and 5938 deaths the week after Thanksgiving (based on data from “Holidays, Birthdays, and Postponement of Cancer Death,” by Young and Hade, Journal of the American Medical Association, Vol. 292, No. 24). If people can postpone death until after Thanksgiving, then the proportion of deaths in the week before should be less than 0.5. Use a 0.05 significance level to test the claim that the proportion of deaths in the week before Thanksgiving is less than 0.5. Based on the result, does there appear to be any indication that people can temporarily postpone death to survive the Thanksgiving holiday?arrow_forward
- Breastmilk and Antioxidants. There is convincing evidence that breastmilk containing antioxidants is important in the prevention of diseases in infants. Researchers A. Xavier et al. studied the effects of storing breastmilk on antioxidant levels in the article “Total Antioxidant Concentrations of Breastmilk—An Eye-Opener to the Negligent” (Journal of Health, Population and Nutrition, Vol. 29, No. 6, pp. 605–611). Samples of breastmilk were taken from women and divided into fresh samples that were immediately tested and the remaining samples that were stored in the refrigerator and tested after 48 hours. A hypothesis test is to be performed to decide whether, on average, stored breastmilk has a lower total antioxidant capacity. a. identify the variable. b. identify the two populations. c. identify the pairs. d. identify the paired-difference variable. e. determine the null and alternative hypotheses. f. classify the hypothesis test as two tailed, left tailed, or right tailed.arrow_forwardSmartphone Battery Life. Battery life is an important issue for many smartphone owners. Public health studies have examined “low-battery anxiety” and acute anxiety called nomophobia that results when a smartphone user’s phone battery charge runs low and then dies (Wall Street Journal, https://www.wsj.com/articles/your-phone-is-almost-out-of-battery-remain-calm-call-a-doctor-1525449283). Battery life between charges for the Samsung Galaxy S9 averages 31 hours when the primary use is talk time and 10 hours when the primary use is Internet applications. Because the mean hours for talk time usage is greater than the mean hours for Internet usage, the question was raised as to whether the variance in hours of usage is also greater when the primary use is talk time. Sample data showing battery life between charges for the two applications follows. Primary Use: Talking35.8 22.2 24.0 32.6 18.5 42.5 28.0 23.8 30.0 22.8 20.3 35.5Primary Use: Internet14.0 12.5 16.4…arrow_forward“Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. Based on your hypothesis tests and confidence intervals, what do you conclude about the effects of second hand smoke? Why?arrow_forward
- “Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. 1. Construct a confidence interval estimate of the difference betwen the mean continen levels fo the two groups of nonsmokers. What confidence level would be appropriate? 2. Find the margin of error E using the formula. 3. What is the confidence interval? Explain the meaning of the confidence interal and what the limit represents.arrow_forwardDetermine the kurtosis if the data given is a sample.arrow_forwardLemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy)” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Lemon Imports 230 265 358 480 530 Crash Fatality Rate 15.9 15.7 15.4 15.3 14.9 Question ---- > Find the critical values of r using α = 0.05 and use test statistic r = -0.959 to determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. Group of answer choices r = ± 0.811, There is enough evidence to Support the Claim r = ± 0.878, There NOT is enough evidence to Support the Claim r = ± 0.811, There NOT is enough evidence to Support the Claim r = ± 0.878, There is enough evidence to Support the Claimarrow_forward
- please help me out. show full working out for better understanding Hereditary hemochromatosis (HH) is a recessively inherited genetic disorder resulting from mutations in the HFE gene. There are several possible mutations of different degrees of importance but the disease expresses itself only when at least 2 arepresent in any one individual. A blood analysis was performed on 3,000 blood samples from newborn babies of Caucasian descent in the state of Michigan, USA. The results showed that 163 of those sampled carried two mutations in the HFE gene. a. What is the proportion in the sample that carry the two mutations of the HFE gene? b. Calculate the 95% confidence interval for the proportion of this population that carries two mutations in the HFE Check the data for the necessary conditions and show full working. c. Interpret your interval in context d. If the researcher wanted to halve (x ½) the margin of error in the confidence interval found, what sample size would be required…arrow_forwardLemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy)” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Lemon Imports 230 265 358 480 530 Crash Fatality Rate 15.9 15.7 15.4 15.3 14.9 Question ---- > Find the critical values of r using α = 0.05 and write Ho and H1 Group of answer choices r = ± 0.878 Ho : ρ = 0 H1: ρ < 0 r = ± 0.811 Ho : ρ = 0 H1: ρ > 0 r = ± 0.878 Ho : ρ = 0 H1: ρ ≠ 0 r = 0.878 Ho : ρ > 0 H1: ρ ≠ 0arrow_forwardApplying the Concepts and SkillsUse the technology of your choice to solve Problems.Smoking and Cotinine. Smoking during pregnancy is hazardousto both the mother and baby. Passive smoking, or inhalation of second-hand smoke, is also a concern. In the article “Detection of Cotinine in Neonate Meconium as a Marker for Nicotine Exposure in Utero” (Eastern Mediterranean Health Journal, Vol. 10, No. 1/2, pp. 96–105), N. Sherif et al. studied whether activesmoking or passive-smoking mothers were passing along harmful chemicals to their babies. The level of cotinine in a newborn’s first meconium, which is the infant’s stool, is reported on the WeissStats site for independent samples of active-, passive-, and nonsmoking mothers. Cotinine levels are measured in nanograms per milliliter (ng/mL). Decide whether presuming that the assumptions of normal populations and equal population standard deviations are met is reasonable.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning