Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data. Program A B C 510 450 600 400 510 620 490 400 570 520 440 490 490 470 590 640 380 630 550 580 Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use a = 0.05. State the null and alternative hypotheses. = OH: Median H: Median Median Median Median Median OH: Median = Median = Median H₂: Median > Median < Median OH: Not all populations of test scores are identical. H: All populations of test scores are identical. All populations of test scores are identical. H: Not all populations of test scores are identical. OH: Median Median Median H₂: Median = Median = Median Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =

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**Title: Comparing Admission Test Preparation Programs Using the Kruskal-Wallis Test**

**Introduction:**
Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data:

**Program Scores:**
- Program A: 510, 400, 490, 520, 470, 640, 550
- Program B: 450, 510, 470, 490, 520, 470, 440, 510, 440, 580
- Program C: 600, 620, 570, 490, 490, 390, 630, 580

**Data Representation:**
The scores are shown in the table below:

| Program | Scores                                    |
|---------|-------------------------------------------|
| A       | 510, 400, 490, 520, 470, 640, 550         |
| B       | 450, 510, 470, 490, 520, 470, 440, 510, 440 |
| C       | 600, 620, 570, 490, 490, 390, 630, 580    |

**Objective:**
Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs.

**Hypotheses:**
State the null and alternative hypotheses.

1. \( H_0 \): Median_A = Median_B = Median_C
   \( H_a \): At least one population median of test scores is different.

Based on the question requirements, the correct null and alternative hypotheses are:
- \( H_0 \): Median_A = Median_B = Median_C
- \( H_a \): At least one population median of test scores is different.

**Procedure:**
1. **Compute the Kruskal-Wallis Test Statistic:**
   Find the value of the test statistic. (Round your answer to two decimal places.)

2. **Consider the Significance Level:**
   Use a significance level of α = 0.05.

3. **Determine the p-value:**
   Find and interpret the p-value. (Round your answer to three decimal places.)

**Results:**
- **Test Statistic Value:** Enter the calculated value here.
- **p-value:** Enter the calculated p-value here.

**Conclusion:**
Based on the p-value compared to the
Transcribed Image Text:**Title: Comparing Admission Test Preparation Programs Using the Kruskal-Wallis Test** **Introduction:** Three admission test preparation programs are being evaluated. Suppose the scores obtained by a sample of 20 people who used the programs provided the following data: **Program Scores:** - Program A: 510, 400, 490, 520, 470, 640, 550 - Program B: 450, 510, 470, 490, 520, 470, 440, 510, 440, 580 - Program C: 600, 620, 570, 490, 490, 390, 630, 580 **Data Representation:** The scores are shown in the table below: | Program | Scores | |---------|-------------------------------------------| | A | 510, 400, 490, 520, 470, 640, 550 | | B | 450, 510, 470, 490, 520, 470, 440, 510, 440 | | C | 600, 620, 570, 490, 490, 390, 630, 580 | **Objective:** Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. **Hypotheses:** State the null and alternative hypotheses. 1. \( H_0 \): Median_A = Median_B = Median_C \( H_a \): At least one population median of test scores is different. Based on the question requirements, the correct null and alternative hypotheses are: - \( H_0 \): Median_A = Median_B = Median_C - \( H_a \): At least one population median of test scores is different. **Procedure:** 1. **Compute the Kruskal-Wallis Test Statistic:** Find the value of the test statistic. (Round your answer to two decimal places.) 2. **Consider the Significance Level:** Use a significance level of α = 0.05. 3. **Determine the p-value:** Find and interpret the p-value. (Round your answer to three decimal places.) **Results:** - **Test Statistic Value:** Enter the calculated value here. - **p-value:** Enter the calculated p-value here. **Conclusion:** Based on the p-value compared to the
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