Report an appropriate hypothesis test and use a 5% significance level. This question is about the second part of Step 4 of the six-step One-way Anova F-test procedure that was taught in this class.  Fill in the blanks appropriately. (ii) Largest sample variance (do not round):        Smallest sample variance (do not round):        Ratio of largest to smallest (one decimal pl

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Report an appropriate hypothesis test and use a 5% significance level.

This question is about the second part of Step 4 of the six-step One-way Anova F-test procedure that was taught in this class. 

Fill in the blanks appropriately.

(ii) Largest sample variance (do not round): 

      Smallest sample variance (do not round): 

      Ratio of largest to smallest (one decimal place): 

The ratio of the largest to the smallest sample variance is less-than-or-equal-to-four so it is safe to assume that the population variances are approx equal.

**One-Way ANOVA**

Data from #13-13 pp.520 of “Applied Statistics and Probability for Engineers” Fourth edition by Douglas C. Montgomery & George C. Runger.

The goal of this experiment was to see if four specific firing temperatures (100, 125, 150, and 175 degrees F) had any effect on the density of a certain type of brick. The units for density are not known. The firing temperatures are being treated as categories rather than quantities.

**Graph Description:**

The graph is a scatter plot illustrating the density of bricks at four different firing temperatures: 100, 125, 150, and 175 degrees F. Each temperature category is represented by a different color: blue for 100, orange for 125, gray for 150, and yellow for 175. The density values on the y-axis range from 21.3 to 22.

**ANOVA: Single Factor**

**Summary Table:**

- **Groups:** The four temperature categories.
- **Count:** Number of observations for each group.
  - 100: 7
  - 125: 4
  - 150: 5
  - 175: 6
- **Sum:** Total sum of densities for each group.
  - 100: 152
  - 125: 86.1
  - 150: 108.6
  - 175: 130.5
- **Average:** Average density for each group.
  - 100: 21.7143
  - 125: 21.525
  - 150: 21.72
  - 175: 21.75
- **Variance:** Variance of densities for each group.
  - 100: 0.0181
  - 125: 0.0158
  - 150: 0.027
  - 175: 0.011

**ANOVA Table:**

- **Source of Variation**
  - Between Groups: 
    - SS (Sum of Squares): 0.1391
    - df (degrees of freedom): 3
    - MS (Mean Square): 0.0464
    - F: 2.6159
    - P-value: 0.0827
    - F crit: 3.1599

  - Within Groups:
    - SS
Transcribed Image Text:**One-Way ANOVA** Data from #13-13 pp.520 of “Applied Statistics and Probability for Engineers” Fourth edition by Douglas C. Montgomery & George C. Runger. The goal of this experiment was to see if four specific firing temperatures (100, 125, 150, and 175 degrees F) had any effect on the density of a certain type of brick. The units for density are not known. The firing temperatures are being treated as categories rather than quantities. **Graph Description:** The graph is a scatter plot illustrating the density of bricks at four different firing temperatures: 100, 125, 150, and 175 degrees F. Each temperature category is represented by a different color: blue for 100, orange for 125, gray for 150, and yellow for 175. The density values on the y-axis range from 21.3 to 22. **ANOVA: Single Factor** **Summary Table:** - **Groups:** The four temperature categories. - **Count:** Number of observations for each group. - 100: 7 - 125: 4 - 150: 5 - 175: 6 - **Sum:** Total sum of densities for each group. - 100: 152 - 125: 86.1 - 150: 108.6 - 175: 130.5 - **Average:** Average density for each group. - 100: 21.7143 - 125: 21.525 - 150: 21.72 - 175: 21.75 - **Variance:** Variance of densities for each group. - 100: 0.0181 - 125: 0.0158 - 150: 0.027 - 175: 0.011 **ANOVA Table:** - **Source of Variation** - Between Groups: - SS (Sum of Squares): 0.1391 - df (degrees of freedom): 3 - MS (Mean Square): 0.0464 - F: 2.6159 - P-value: 0.0827 - F crit: 3.1599 - Within Groups: - SS
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