### Investigating Blood Type Frequencies at a Plasma CenterThis exercise examines the frequencies of different blood types among 200 people who volunteered at a plasma center. The data is presented in the table below:| **Blood Type** | **O** | **A** | **B** | **AB** | **Total** ||:--------------:|:-----:|:-----:|:-----:|:------:|:---------:|| **Frequency** | 82 | 80 | 20 | 18 | 200 |We aim to determine whether these four blood types are equally likely. We will conduct a hypothesis test at a significance level of \( \alpha = 0.05 \).#### Step-by-Step Hypothesis Testing:1. **Identify the Parameters:** The null and alternative hypotheses are based around the question of whether the four blood type distributions are equal in the population.2. **Null Hypothesis (\( H_0 \)):** The null hypothesis posits that the proportions of the different blood types are equal. Mathematically, it can be expressed as: \[ H_0: p_O = p_A = p_B = p_{AB} = \frac{1}{4} \]3. **Alternative Hypothesis (\( H_A \)):** The alternative hypothesis is that at least one blood type proportion is different from the rest. Formally written as: \[ H_A: \text{At least one } p_i \text{ is different} \]4. **Test Statistic:** The test statistic for this goodness-of-fit test, typically a Chi-Square statistic, is calculated based on the observed frequencies and the expected frequencies under the null hypothesis.5. **Rejection Region:** The rejection region is determined based on the Chi-Square distribution with degrees of freedom \( df = k - 1 \), where \( k \) is the number of categories (4 in this case). For \(\alpha = 0.05\) and \( df = 3 \), we refer to the critical value from Chi-Square tables. ![Rejection Region Graph](https://latex.codecogs.com/svg.image?\begin{array}{|c|c|c|c|}\hline&\textbf{df}&3\\\textbf{\

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Description: ### Investigating Blood Type Frequencies at a Plasma CenterThis exercise examines the frequencies of different blood types among 200 people who volunteered at a plasma center. The data is presented in the table below:| **Blood Type** | **O** | **A**

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1. The frequencies of different blood types of 200 people who volunteered at a plasma center is given in the table. Blood Type O А frequency Are these four blood types equally likely? Use a = 0.05. АВ | Total 82 80 20 18 200 1. Identify the parame ters 2 Null hypothe sis 3. Altemative hypothesis 4. Test Statistics 6. Conclusion 5. Rejection region

1. The frequencies of different blood types of 200 people who volunteered at a plasma center is given in the table. Blood Type O А frequency Are these four blood types equally likely? Use a = 0.05. АВ | Total 82 80 20 18 200 1. Identify the parame ters 2 Null hypothe sis 3. Altemative hypothesis 4. Test Statistics 6. Conclusion 5. Rejection region

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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