### Understanding Hypothesis Testing for Cancer Research#### Question 1Assume you are conducting a hypothesis test to determine if pesticides cause cancer in rural areas. The hypotheses are:- **Null hypothesis (H₀):** No cancer.- **Alternate hypothesis (H₁):** Cancer.Select if the result for Box C is correct, a Type I error, a Type II error, or if there is insufficient information to make the decision.##### **H₀:** no cancer ##### **H₁:** cancerThe matrix below illustrates the potential outcomes of the hypothesis test:| **Reality** | Null is true (i.e., no cancer) | Alternate is true (i.e., cancer) ||------------------------------------|---------------------------------|--------------------------------|| **Decision: Accept the null hypothesis** (i.e., test is negative for cancer) | A | B || **Decision: Reject the null hypothesis** (i.e., test is positive for cancer) | C | D |**Explanation of the Matrix:**- **Box A:** Correct decision. The test indicates no cancer, and indeed, there is no cancer.- **Box B:** Type II error. The test indicates no cancer, but there actually is cancer (false negative).- **Box C:** Type I error. The test indicates cancer, but there actually is no cancer (false positive).- **Box D:** Correct decision. The test indicates cancer, and indeed, there is cancer. This is a decision matrix illustrating the potential outcomes of a hypothesis test. Specifically, it deals with testing for cancer. The matrix is structured to show the relationship between the true state of nature (whether the null hypothesis is true or false) and the decision made based on the test results. Here is the detailed explanation:### Decision Matrix#### Columns:1. **Null is true (i.e., no cancer)**2. **Alternative is true (i.e., cancer)**#### Rows:1. **Accept the null hypothesis (i.e., test is negative for cancer)**2. **Reject the null hypothesis (i.e., test is positive for cancer)**#### Outcomes:- **A (First Row, First Column):** Accept the null hypothesis when the null hypothesis is true. This represents a correct decision, as the test correctly identifies the absence of cancer. - **B (First Row, Second Column):** Accept the null hypothesis when the alternative hypothesis is true. This represents a Type II error, as the test incorrectly concludes no cancer when cancer is present.- **C (Second Row, First Column):** Reject the null hypothesis when the null hypothesis is true. This represents a Type I error, as the test incorrectly identifies cancer when there is none.- **D (Second Row, Second Column):** Reject the null hypothesis when the alternative hypothesis is true. This represents a correct decision, as the test correctly identifies the presence of cancer.### Question:- **Correct**- **Type I error**- **Type II error**- **There is insufficient evidence**

Box C indicates that the null hypothesis is rejected, when the null hypothesis is actually true.

Assume you are conducting a hypothesis test to determine if pesticides cause cancer in rural areas. The hypotheses are: The null hypothesis is no cancer. The alternate hypothesis is cancer. Select if the result for Box C is correct, a Type I error, a Type II error or if there is insufficient information to make the decision.

Assume you are conducting a hypothesis test to determine if pesticides cause cancer in rural areas. The hypotheses are: The null hypothesis is no cancer. The alternate hypothesis is cancer. Select if the result for Box C is correct, a Type I error, a Type II error or if there is insufficient information to make the decision.

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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