Complete the following ANOVA summary table. There are 3 groups with 5 samples each. Use a signifcance level of 0.10 Ho: All population means are equal Ha: At least one population mean is different from the others (claim) Round all values to 2 decimal places SS MS F Between 23.66 Within

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**ANOVA Summary Table Completion**

In this exercise, we complete an ANOVA (Analysis of Variance) summary table. There are three groups, each with five samples. The significance level used is 0.10.

**Hypotheses:**
- \( H_0 \): All population means are equal.
- \( H_a \): At least one population mean is different from the others (claim).

**Table:**

\[
\begin{array}{|c|c|c|c|c|}
\hline
 & \text{SS} & \text{df} & \text{MS} & F \\
\hline
\text{Between} & 23.66 & & & \\
\hline
\text{Within} & & & & \\
\hline
\text{TOTAL} & 74.66 & & & \\
\hline
\end{array}
\]

**Instructions:**
- Round all values to 2 decimal places.

**Steps:**
1. Calculate the degrees of freedom (df) for both Between and Within groups.
2. Calculate the mean square (MS) by dividing SS by df.
3. Calculate the F-ratio.

**Decision Making:**
- Use the F distribution table to find the critical value \( F_0 \).
- Determine whether to:
  - Reject the null hypothesis if there is enough evidence to support that at least one mean is different.
  - Fail to reject the null hypothesis if there is not enough evidence to support the claim.

Ensure all steps of calculations adhere to statistical methodologies for ANOVA.
Transcribed Image Text:**ANOVA Summary Table Completion** In this exercise, we complete an ANOVA (Analysis of Variance) summary table. There are three groups, each with five samples. The significance level used is 0.10. **Hypotheses:** - \( H_0 \): All population means are equal. - \( H_a \): At least one population mean is different from the others (claim). **Table:** \[ \begin{array}{|c|c|c|c|c|} \hline & \text{SS} & \text{df} & \text{MS} & F \\ \hline \text{Between} & 23.66 & & & \\ \hline \text{Within} & & & & \\ \hline \text{TOTAL} & 74.66 & & & \\ \hline \end{array} \] **Instructions:** - Round all values to 2 decimal places. **Steps:** 1. Calculate the degrees of freedom (df) for both Between and Within groups. 2. Calculate the mean square (MS) by dividing SS by df. 3. Calculate the F-ratio. **Decision Making:** - Use the F distribution table to find the critical value \( F_0 \). - Determine whether to: - Reject the null hypothesis if there is enough evidence to support that at least one mean is different. - Fail to reject the null hypothesis if there is not enough evidence to support the claim. Ensure all steps of calculations adhere to statistical methodologies for ANOVA.
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