I need help with 6 and 7 ---### Blood Type and COVID-19 Susceptibility**Introduction:**A group of researchers in Wuhan, China, investigated the relationship between contracting the novel coronavirus and patients' blood type. The population in Wuhan has a blood type distribution as shown in the table below. The researchers categorized 375 patients who had contracted coronavirus by blood type.**Population and Patient Distribution:**| Blood Type | Population Percentage | COVID-19 Patients ||------------|-----------------------|-------------------|| Type A | 33% | 115 || Type B | 24% | 101 || Type AB | 9% | 41 || Type O | 34% | 118 || **Total** | **100%** | **375** |**Instructions:**Round all calculated values in this problem to 4 decimal places.---**1. Calculate Expected Values**Calculate the expected values for the hypothesis test. Enter these values in the table below:| Blood Type | Expected Value ||------------|----------------|| Type A | 123.75 || Type B | 90 || Type AB | 33.75 || Type O | 127.5 |**2. Hypothesis Testing**The researchers wonder if, in Wuhan, COVID-19 patients have a different distribution of blood type than the general population of Wuhan. Express this research question in terms of a null and alternative hypothesis.- **Null Hypothesis (H₀):** The distribution of blood type of COVID-19 patients is **the same as** the population. Any observed difference **is** due to chance.- **Alternative Hypothesis (H₁):** The distribution of blood type of COVID-19 patients is **different from** the population. Any observed difference **is not** due to chance.---To proceed with the analysis, calculate the expected frequencies assuming the null hypothesis is true, then compare them with the observed frequencies using a chi-square test.This data is critical for understanding any significant differences between the blood type distribution of COVID-19 patients and the general population, which can help in medical research and public health decisions.Continue to practice with similar datasets to enhance your statistical analysis skills.--- ### Hypothesis Testing for Blood Type Distribution in COVID-19 Patients in Wuhan**2. Null and Alternative Hypotheses**The researchers question if the distribution of blood types in COVID-19 patients in Wuhan is different from that of the general population of Wuhan. This is expressed in terms of the following hypotheses: - **Null Hypothesis ($H_0$)**: The distribution of blood type of COVID-19 patients is **the same as** the population. Any observed difference is **due to** chance.- **Alternative Hypothesis ($H_A$)**: The distribution of blood type of COVID-19 patients is **different from** the population. Any observed difference is **not due to** chance.**3. Analysis of Contributions to the Test Statistic**The research examines which blood type, A or O, contributes more to the test statistic. Based on the input:- **Blood type O** is identified as contributing more to the test statistic.**4. Calculating the Test Statistic**The calculated chi-squared ($\chi^2$) test statistic value is:\[ \chi^2 = 4.2283 \]**5. Degrees of Freedom**The degrees of freedom (df) for this test is given as:\[ d_f = 3 \]**6. Calculating the p-Value**The p-value corresponding to the test statistic is:\[ p = 0.47568 \]**7. Conclusion Based on the p-Value**With the given p-value, we state that:- The evidence against the null hypothesis is **extremely strong**.In conclusion, these statistical results are useful for determining whether the observed blood type distribution in COVID-19 patients is significantly different from that of the general population in Wuhan, providing critical insights into potential associations between blood type and COVID-19 infection.

Answered: 6. Calculate the p-value for this test.…

6. Calculate the p-value for this test. p = 0.475687 7. Based on the above p-value, we have extremely strong evidence against the null hypothesis.

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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I need help with 6 and 7

---

### Blood Type and COVID-19 Susceptibility

**Introduction:**
A group of researchers in Wuhan, China, investigated the relationship between contracting the novel coronavirus and patients' blood type. The population in Wuhan has a blood type distribution as shown in the table below. The researchers categorized 375 patients who had contracted coronavirus by blood type.

**Population and Patient Distribution:**

| Blood Type | Population Percentage | COVID-19 Patients |
|------------|-----------------------|-------------------|
| Type A | 33% | 115 |
| Type B | 24% | 101 |
| Type AB | 9% | 41 |
| Type O | 34% | 118 |
| **Total** | **100%** | **375** |

**Instructions:**
Round all calculated values in this problem to 4 decimal places.

---

**1. Calculate Expected Values**

Calculate the expected values for the hypothesis test. Enter these values in the table below:

| Blood Type | Expected Value |
|------------|----------------|
| Type A | 123.75 |
| Type B | 90 |
| Type AB | 33.75 |
| Type O | 127.5 |

**2. Hypothesis Testing**

The researchers wonder if, in Wuhan, COVID-19 patients have a different distribution of blood type than the general population of Wuhan. Express this research question in terms of a null and alternative hypothesis.

- **Null Hypothesis (H₀):** The distribution of blood type of COVID-19 patients is **the same as** the population. Any observed difference **is** due to chance.

- **Alternative Hypothesis (H₁):** The distribution of blood type of COVID-19 patients is **different from** the population. Any observed difference **is not** due to chance.

---

To proceed with the analysis, calculate the expected frequencies assuming the null hypothesis is true, then compare them with the observed frequencies using a chi-square test.

This data is critical for understanding any significant differences between the blood type distribution of COVID-19 patients and the general population, which can help in medical research and public health decisions.

Continue to practice with similar datasets to enhance your statistical analysis skills.

---

### Hypothesis Testing for Blood Type Distribution in COVID-19 Patients in Wuhan

**2. Null and Alternative Hypotheses**

The researchers question if the distribution of blood types in COVID-19 patients in Wuhan is different from that of the general population of Wuhan. This is expressed in terms of the following hypotheses:

- **Null Hypothesis ($H_0$)**: The distribution of blood type of COVID-19 patients is **the same as** the population. Any observed difference is **due to** chance.
- **Alternative Hypothesis ($H_A$)**: The distribution of blood type of COVID-19 patients is **different from** the population. Any observed difference is **not due to** chance.

**3. Analysis of Contributions to the Test Statistic**

The research examines which blood type, A or O, contributes more to the test statistic. Based on the input:

- **Blood type O** is identified as contributing more to the test statistic.

**4. Calculating the Test Statistic**

The calculated chi-squared ($\chi^2$) test statistic value is:

\[ \chi^2 = 4.2283 \]

**5. Degrees of Freedom**

The degrees of freedom (df) for this test is given as:

\[ d_f = 3 \]

**6. Calculating the p-Value**

The p-value corresponding to the test statistic is:

\[ p = 0.47568 \]

**7. Conclusion Based on the p-Value**

With the given p-value, we state that:

- The evidence against the null hypothesis is **extremely strong**.

In conclusion, these statistical results are useful for determining whether the observed blood type distribution in COVID-19 patients is significantly different from that of the general population in Wuhan, providing critical insights into potential associations between blood type and COVID-19 infection.

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