I need help with 3 and 4 **Minority Models - Educational Analysis****Introduction:**Negative stereotypical depiction of minorities or their exclusion from advertisements in mainstream media has been found to have harmful social effects. Researchers are interested in answering the following question:*Is the proportion of magazine advertisements portraying each racial group different from its proportion of the U.S. population?***Study Overview:**The observed data in the table below is consistent with data collected from an analysis of magazine advertisements from 1993 and 1994. The table summarizes the frequency of the appearance of models in a total of 1527 advertisements.The population distribution values were taken from the 1990 census data.**Data Table:**The data table provided displays both the U.S. Census data percentages from 1990 and the observed data for the four racial groups. | | African Americans | Asian Americans | Hispanic Americans | White Americans ||---------------------|-------------------|-----------------|--------------------|-----------------|| **1990 Census data (%)** | 12.1% | 3.3% | 9.0% | 75.6% || **Observed Data** | 151 | 74 | 80 | 1222 |**Instructions:****1. State the Hypotheses**Select the phrases to complete the null and alternative hypotheses for this research situation.- Null Hypothesis ($H_0$): The proportion of magazine advertisements portraying each racial group is **the same as** its proportion of the U.S. population.- Alternative Hypothesis ($H_A$): The proportion of magazine advertisements portraying each racial group is **different from** its proportion of the U.S. population.**2. Determine the Suitable Test**What type of test should the researchers use?- $ \chi^2 $ goodness of fit test**3. Validity Conditions**Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.- $ \square $ There must be an expected count of at least 5 for each level of the categorical variable.- $ \square $ Each case in the table must be independent of all other cases.- $ \square $ There must be at least 3 levels of the categorical variable.**Conclusion:**Round all calculated values to 4 decimal places where appropriate and ensure all conditions for the selected hypothesis test are met for ### Statistical Testing in Research#### 2. What type of test should the researchers use?A. t-test for a sample mean B. t-test for the slope of the regression line C. **χ² goodness of fit test** (Selected) D. χ² test of independence E. Z-test for one population proportion #### 3. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.A. There must be at least 10 "success" and 10 "failure" observations. B. **There must be an expected count of at least 5 for each level of the categorical variable.** (Selected) C. Each case in the table must be independent of all other cases. D. There must be at least 3 levels of the categorical variable. E. The sample size must be at least 30 or the population data must be normally distributed. #### 4. What is the degrees of freedom for this test?**0**#### 5. Under the null hypothesis model, what is the expected count for Asian Americans?**50.391**#### 6. Calculate the contribution to the test statistic for Asian Americans:**11.0612**#### 7. Calculate the test statistic for this procedure:χ² = \_\_\_\_#### 8. Based on the test statistic, calculate the p-value:p-value = \_\_\_\_#### 9. The results of this test indicate that we have \_\_\_\_ evidence against the null hypothesis.**Little** evidence against the null hypothesis.---This educational example highlights the steps involved in conducting a hypothesis test using the χ² goodness of fit test. It includes determining the type of test required, validating the assumptions, calculating degrees of freedom, and interpreting the expected counts and contributions to the test statistic. The final steps involve calculating the test statistic and p-value, which help in determining the strength of evidence against the null hypothesis.Diagrams and graphs explaining the procedure in more detail can complement this textual walkthrough, ensuring a comprehensive learning experience for students.

3. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply. A. There must be at least 10 "success" and 10 "failure" observations. B. There must be an expected count of at least 5 for each level of the categorical variable. C. Each case in the table must be independent of all other cases. D. There must be at least 3 levels of the categorical variable. )E. The sample size must be at least 30 or the population data must be normally distributed. 4. What is the degrees of freedom for this test? 0

3. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply. A. There must be at least 10 "success" and 10 "failure" observations. B. There must be an expected count of at least 5 for each level of the categorical variable. C. Each case in the table must be independent of all other cases. D. There must be at least 3 levels of the categorical variable. )E. The sample size must be at least 30 or the population data must be normally distributed. 4. What is the degrees of freedom for this test? 0

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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Question

I need help with 3 and 4

**Minority Models - Educational Analysis**

**Introduction:**
Negative stereotypical depiction of minorities or their exclusion from advertisements in mainstream media has been found to have harmful social effects. Researchers are interested in answering the following question:

*Is the proportion of magazine advertisements portraying each racial group different from its proportion of the U.S. population?*

**Study Overview:**
The observed data in the table below is consistent with data collected from an analysis of magazine advertisements from 1993 and 1994. The table summarizes the frequency of the appearance of models in a total of 1527 advertisements.

The population distribution values were taken from the 1990 census data.

**Data Table:**
The data table provided displays both the U.S. Census data percentages from 1990 and the observed data for the four racial groups.

| | African Americans | Asian Americans | Hispanic Americans | White Americans |
|---------------------|-------------------|-----------------|--------------------|-----------------|
| **1990 Census data (%)** | 12.1% | 3.3% | 9.0% | 75.6% |
| **Observed Data** | 151 | 74 | 80 | 1222 |

**Instructions:**

**1. State the Hypotheses**
Select the phrases to complete the null and alternative hypotheses for this research situation.

- Null Hypothesis ($H_0$): The proportion of magazine advertisements portraying each racial group is **the same as** its proportion of the U.S. population.
- Alternative Hypothesis ($H_A$): The proportion of magazine advertisements portraying each racial group is **different from** its proportion of the U.S. population.

**2. Determine the Suitable Test**
What type of test should the researchers use?

- $ \chi^2 $ goodness of fit test

**3. Validity Conditions**
Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.
- $ \square $ There must be an expected count of at least 5 for each level of the categorical variable.
- $ \square $ Each case in the table must be independent of all other cases.
- $ \square $ There must be at least 3 levels of the categorical variable.

**Conclusion:**
Round all calculated values to 4 decimal places where appropriate and ensure all conditions for the selected hypothesis test are met for

### Statistical Testing in Research

#### 2. What type of test should the researchers use?
A. t-test for a sample mean
B. t-test for the slope of the regression line
C. **χ² goodness of fit test** (Selected)
D. χ² test of independence
E. Z-test for one population proportion

#### 3. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.
A. There must be at least 10 "success" and 10 "failure" observations.
B. **There must be an expected count of at least 5 for each level of the categorical variable.** (Selected)
C. Each case in the table must be independent of all other cases.
D. There must be at least 3 levels of the categorical variable.
E. The sample size must be at least 30 or the population data must be normally distributed.

#### 4. What is the degrees of freedom for this test?
**0**

#### 5. Under the null hypothesis model, what is the expected count for Asian Americans?
**50.391**

#### 6. Calculate the contribution to the test statistic for Asian Americans:
**11.0612**

#### 7. Calculate the test statistic for this procedure:
χ² = \_\_\_\_

#### 8. Based on the test statistic, calculate the p-value:
p-value = \_\_\_\_

#### 9. The results of this test indicate that we have \_\_\_\_ evidence against the null hypothesis.
**Little** evidence against the null hypothesis.

---

This educational example highlights the steps involved in conducting a hypothesis test using the χ² goodness of fit test. It includes determining the type of test required, validating the assumptions, calculating degrees of freedom, and interpreting the expected counts and contributions to the test statistic. The final steps involve calculating the test statistic and p-value, which help in determining the strength of evidence against the null hypothesis.

Diagrams and graphs explaining the procedure in more detail can complement this textual walkthrough, ensuring a comprehensive learning experience for students.

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