### Colonoscopy as a Screening Test for Colon CancerA colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. One study¹ provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01?¹Zauber, et.al., "Colonscopic Polypectomy and Long-Term Prevention of Colorectal-Cancer Deaths," *New England Journal of Medicine*, 2012; 366: 687-696.### Hypothesis Testing**(a) What are the null and alternative hypotheses?**Below the text, there is a graphical tool for formulating hypotheses, allowing users to select various symbols and notation to build their hypotheses. Symbols and notations available include:- Equality (=)- Inequality (≠)- Less than (<)- Greater than (>)- Mean (μ)- Different population means (μ₁, μ₂)- Proportion (p)- Sample means (x̄₁, x̄₂)- Specific sample statistics (e.g., 0.01)- Correlation coefficient (ρ)- Sample proportions (p̂₁, p̂₂)- Linear correlation coefficient (r)**Hypotheses to test:**- Null Hypothesis (H₀): p = 0.01 (The proportion of people who die from colon cancer after having polyps removed in a colonoscopy is equal to 0.01)- Alternative Hypothesis (Hₐ): p < 0.01 (The proportion of people who die from colon cancer after having polyps removed in a colonoscopy is less than 0.01)By formulating these hypotheses, researchers can use statistical tests to determine whether the evidence supports that the colonoscopy procedure significantly reduces the risk of death from colon cancer compared to the expected proportion without the procedure.

Given values, p = 0.01n = 2602x = 12

A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. One study' provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01? 'Zauber, et.al., "Colonoscopic Polypectomy and Long-Term Prevention of Colorectal-Cancer Deaths," New England Journal of Medicine, 2012; 366: 687-696. (a) What are the null and alternative hypotheses? :: p : Pi : P2 :: 0.01 : Pi : P2 :: :: ::

A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. One study' provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01? 'Zauber, et.al., "Colonoscopic Polypectomy and Long-Term Prevention of Colorectal-Cancer Deaths," New England Journal of Medicine, 2012; 366: 687-696. (a) What are the null and alternative hypotheses? :: p : Pi : P2 :: 0.01 : Pi : P2 :: :: ::

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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