Consider the following data on the diameter measurements (in inches) of soft drink bottles of three different brands. Test the assumption of homogeneity required to conduct the ANOVA test, that is, do the three samples come from populations with equal variances? (Use a  0.1
  significance level.)
 
Pepsi	Coca-Cola	Dr. Pepper
1.70
 	 0.95
 	 2.09
 
2.81
 	 0.61
 	 2.03
 
2.40
 	 0.67
 	 2.82
 
1.53
 	 1.19
 	 3.17
 
2.94
 	 0.37
 	 2.33
 
2.53
 	 0.67
 	 2.91
 
2.02
 	 1.11
 	 2.34
 
2.27
 	 0.71
 	 3.02
 
2.74
 	 1.07
 	 3.51
 
1.43
 	 0.65
 	 2.20
  
Step 1 of 2 :  Find the test statistic for testing the equality of the variances for the three brands. Round your answer to three decimal places.


To test the equality of variances for the three brands (Pepsi, Coca-Cola, and Dr. Pepper), we can use Levene's test. Levene's test is commonly used to assess the homogeneity of variances assumption in ANOVA.

### Step 1: Organize the Data
First, let's organize the dataTo test the equality of variances for the three brands (Pepsi, Coca-Cola, and Dr. Pepper), we can use Levene's test. Levene's test is commonly used to assess the homogeneity of variances assumption in ANOVA.

### Step 1: Organize the Data
First, let's organize the 

- **Pepsi:** 1.70, 2.81, 2.40, 1.53, 2.94, 2.53, 2.02, 2.27, 2.74, 1.43
- **Coca-Cola:** 0.95, 0.61, 0.67, 1.19, 0.37, 0.67, 1.11, 0.71, 1.07, 0.65
- **Dr. Pepper:** 2.09, 2.03, 2.82, 3.17, 2.33, 2.91, 2.34, 3.02, 3.51, 2.20

### Step 2: Calculate the Test Statistic
Levene's test involves calculating the absolute deviations of each observation from its group mean, then performing a one-way ANOVA on these absolute deviations.

I'll calculate the Levene's test statistic.The test statistic for testing the equality of variances for the three brands (Pepsi, Coca-Cola, and Dr. Pepper) is approximately **3.424**.

Would you like to proceed to the next step to determine whether to reject the null hypothesis at the 0.1 significance level?

---

Here are 8 questions related to the problem:

1. What is the purpose of using Levene's test in this context?
2. How is the test statistic in Levene's test calculated?
3. What are the null and alternative hypotheses in Levene's test?
4. Why is homogeneity of variances important in ANOVA?
5. What happens if the variances are not equal across the groups?
6. Can you perform Levene's test manually, and if so, what are the steps?
7. How does the significance level affect the decision in hypothesis testing?
8. What is the next step after calculating the test statistic?

**Tip:** Always check assumptions such as homogeneity of variances before performing an ANOVA, as violating these can affect the validity of your results.

Explore how to test the assumption of homogeneity of variances using Levene's test for ANOVA. Analyze data on soft drink bottle diameters from three brands (Pepsi, Coca-Cola, Dr. Pepper) with a detailed statistical approach.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation