An experiment was carried out to compare electrical resistivity for six different low-permeability concrete bridge deck mixtures. There were 26 measurements on concrete cylinders for eam these were obtained 28 days after casting. The entries in the accompanying ANOVA table are based on information in an article. Fill in the remaining entries. (Round your answer for f to t places.) You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. Sum of Squares Source Mixture 5 Error Total 150 155 df ✓ 5664.475 # Ho: H₁ H₂ H3 H4 H5 H6 Ha: at least two μ's are equal Ho: H₁ H₂ H3 H4 H5 H6 H₂: all six μ's are equal Test appropriate hypotheses at level 0.05. State the appropriate hypotheses. (Let μ, the true mean electrical resistivity for the /th mixture.) O Ho: H₁ H₂ H3 H4 H5 = 46 H: at least two μ's are unequal Ho: H₁ = H₂ = H3 = H4=H5 = 16 Ha: all six μ's are unequal Mean Square ✓ 13.969 f

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**ANOVA Analysis of Electrical Resistivity for Concrete Mixtures**

An experiment was conducted to compare electrical resistivity for six different low-permeability concrete bridge deck mixtures. Each mixture was measured 26 times on concrete cylinders, 28 days post-casting. The table below represents an ANOVA (Analysis of Variance) based on data from an article. Complete the missing entries, rounding the f value to two decimal places.

**ANOVA Table:**
| Source   | df  | Sum of Squares | Mean Square | f      |
|----------|-----|----------------|-------------|--------|
| Mixture  | 5   |                |             |        |
| Error    | 150 |                | 13.969      |        |
| Total    | 155 | 5664.475       |             |        |

**Instructions:**
Use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question.

**Hypothesis Testing at Level 0.05:**
State the appropriate hypotheses. Let \( \mu_i \) represent the true mean electrical resistivity for the i-th mixture.

- \( H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5 = \mu_6 \)
- \( H_a \): at least two \( \mu_i \)'s are unequal

**Select the Appropriate Hypothesis:**
- \( H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5 = \mu_6 \)
- \( H_a \): at least two \( \mu_i \)'s are unequal

(The correct option is selected with a checkmark.)

**Test Statistic Calculation:**
Round your answer to two decimal places for f = ...

**P-Value Interpretation:**
Discuss what can be concluded about the p-value for the test.

**Explanation:**
The ANOVA table analysis involves testing the equality of means for different groups. The mean square values are calculated for both the treatments (mixtures) and the error, and the f statistic is determined. The hypothesis test checks if there is a statistically significant difference among the means of the mixtures, where a significant f value suggests rejecting the null hypothesis.
Transcribed Image Text:**ANOVA Analysis of Electrical Resistivity for Concrete Mixtures** An experiment was conducted to compare electrical resistivity for six different low-permeability concrete bridge deck mixtures. Each mixture was measured 26 times on concrete cylinders, 28 days post-casting. The table below represents an ANOVA (Analysis of Variance) based on data from an article. Complete the missing entries, rounding the f value to two decimal places. **ANOVA Table:** | Source | df | Sum of Squares | Mean Square | f | |----------|-----|----------------|-------------|--------| | Mixture | 5 | | | | | Error | 150 | | 13.969 | | | Total | 155 | 5664.475 | | | **Instructions:** Use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. **Hypothesis Testing at Level 0.05:** State the appropriate hypotheses. Let \( \mu_i \) represent the true mean electrical resistivity for the i-th mixture. - \( H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5 = \mu_6 \) - \( H_a \): at least two \( \mu_i \)'s are unequal **Select the Appropriate Hypothesis:** - \( H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5 = \mu_6 \) - \( H_a \): at least two \( \mu_i \)'s are unequal (The correct option is selected with a checkmark.) **Test Statistic Calculation:** Round your answer to two decimal places for f = ... **P-Value Interpretation:** Discuss what can be concluded about the p-value for the test. **Explanation:** The ANOVA table analysis involves testing the equality of means for different groups. The mean square values are calculated for both the treatments (mixtures) and the error, and the f statistic is determined. The hypothesis test checks if there is a statistically significant difference among the means of the mixtures, where a significant f value suggests rejecting the null hypothesis.
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