Mathematics-Statistics

Show All Work for Full Credit Colonoscopy is a medical act that is contrived to discover and eject precancerous lesions in the colon precedently they befit cancerous. In a illustration of 51, 460 inhabitants extraneously colorectal cancer, 5043 had previously had a colonoscopy, and in a illustration of 10,292 inhabitants diagnosed after a while colorectal cancer, 720 had previously had a colonoscopy.  Construct a 95% trust interim for the dissent in the symmetrys of inhabitants who had colonoscopies shapeclose those who were diagnosed after a while colorectal cancer and those who were not.  Does the trust interim controvert the right that the symmetry of inhabitants who entertain had colonoscopies is the identical shapeclose those after a while colorectal cancer and those extraneously?  The attention of benzene was measured in units of milligrams per liter for a sincere chance illustration of five specimens of untreated wastesoak produced at a gas opportunity. The illustration balance was 7.8 after a while a illustration gauge gap of 1.4. Seven specimens of composition wastesoak had an medium benzene attention of 3.2 after a while a gauge gap of 1.7. It is self-possessed to feign twain illustrations follow from populations that are closely ordinary. Can you complete that the balance benzene attention is close in treated soak than in untreated soak? Use the α =0.05 flatten of feeling.  The National Soundness and Nutrition Examination Surveys (NHANES) are contrived to assess the soundness and nutritional foundation of adults and consequence in the United States. According to a late NHANES view, the balance climax of adult men in the United States is 69.7 inches, after a while a gauge gap of 3 inches. A sociologist believes that taller men may be over likely to be promoted to positions of example, so the balance climax µ of manly profession magistrates may be greater than the balance climax of the total manly population. A sincere chance illustration of 100 manly profession magistrates has a balance climax of 69.9 inches. Feign that the gauge gap of manly magistrate climaxs is σ = 3 inches. Can we complete that manly profession magistrates are taller, on the medium, than the unconcealed population at the α =0.05 flatten?