## Evaluating the Success of a New Cancer TreatmentSuppose a cancer treatment successfully cures the disease in 67% of cases. An oncologist is developing a new treatment that they believe will cure this cancer at a higher rate.### Hypothesis TestingTo test the hypothesis that the new treatment is more successful than the previous treatment, a random sample of 20 people is collected.- If the number of people in the sample that are cured is **less than 16**, we will not reject the null hypothesis that \( p = 0.67 \).- Otherwise, we will conclude that \( p > 0.67 \).**Round all answers to 4 decimals.**### Statistical Calculations1. **Calculate \( \alpha = P(\text{Type I Error}) \)** assuming that \( p = 0.67 \). *Use the Binomial Distribution.*2. **Calculate \( \beta = P(\text{Type II Error})** for the alternative \( p = 0.82 \). *Use the Binomial Distribution.*3. **Find the power of the test for the alternative \( p = 0.82 \). *Use the Binomial Distribution.* In this study, \( \alpha \) represents the probability of incorrectly rejecting the null hypothesis when it is true (Type I Error). Whereas \( \beta \) represents the probability of failing to reject the null hypothesis when the alternative hypothesis is true (Type II Error). The power of the test, calculated as \( 1 - \beta \), indicates the test's ability to correctly detect an effect when there is one. These calculations help determine the efficacy of the new cancer treatment in comparison to the current one.

Given information: Null hypothesis H0: p=0.67Alternate hypothesis HA: p>0.67

Answered: Suppose a cancer treatment successfully…

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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