A football coach claims that players can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes' strength. Use a = 0.05. Assume that the distribution is normally distributed. ATHELETE 1 3 4 15 6 7 9 BEFORE 215 240 188 212 275 260 225 200 185 AFTER 225 245 188 210 282 275 230 195 190

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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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**Title: Testing the Effectiveness of a Strength Supplement for Athletes**

A football coach claims that players can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes’ strength.

**Use α = 0.05. Assume that the distribution is normally distributed.**

| **ATHLETE** | **1** | **2** | **3** | **4** | **5** | **6** | **7** | **8** | **9** |
|-------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| **BEFORE**  | 215   | 240   | 188   | 212   | 275   | 260   | 225   | 200   | 185   |
| **AFTER**   | 225   | 245   | 188   | 210   | 282   | 275   | 230   | 195   | 190   |

**Use any method but follow the PHANTOMS acronym:**

1. **P - Parameter Statement**
    - Define the parameter of interest.

2. **H - Hypotheses**
    - State the null and alternative hypotheses.

3. **A - Assumptions & Conditions**
    - Verify the assumptions and conditions required for the test.

4. **N - Name the Test**
    - Specify the appropriate statistical test to be used.

5. **T - Test Statistic**
    - Calculate the test statistic.

6. **O - Obtain the P-Value or Critical Value**
    - Determine the P-value or the critical value for the test.

7. **M - Make a Decision about the Null Hypothesis**
    - Compare the test statistic to the critical value or use the P-value to make a decision.

8. **S - State Your Conclusion About the Claim**
    - Conclude whether there is enough evidence to support the claim that the supplement is effective in increasing the athletes’ strength.

**Graphical Explanation:**

There are no graphs or diagrams included in the image, but it presents a table comparing the bench press strength (in unspecified units
Transcribed Image Text:**Title: Testing the Effectiveness of a Strength Supplement for Athletes** A football coach claims that players can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletes’ strength. **Use α = 0.05. Assume that the distribution is normally distributed.** | **ATHLETE** | **1** | **2** | **3** | **4** | **5** | **6** | **7** | **8** | **9** | |-------------|-------|-------|-------|-------|-------|-------|-------|-------|-------| | **BEFORE** | 215 | 240 | 188 | 212 | 275 | 260 | 225 | 200 | 185 | | **AFTER** | 225 | 245 | 188 | 210 | 282 | 275 | 230 | 195 | 190 | **Use any method but follow the PHANTOMS acronym:** 1. **P - Parameter Statement** - Define the parameter of interest. 2. **H - Hypotheses** - State the null and alternative hypotheses. 3. **A - Assumptions & Conditions** - Verify the assumptions and conditions required for the test. 4. **N - Name the Test** - Specify the appropriate statistical test to be used. 5. **T - Test Statistic** - Calculate the test statistic. 6. **O - Obtain the P-Value or Critical Value** - Determine the P-value or the critical value for the test. 7. **M - Make a Decision about the Null Hypothesis** - Compare the test statistic to the critical value or use the P-value to make a decision. 8. **S - State Your Conclusion About the Claim** - Conclude whether there is enough evidence to support the claim that the supplement is effective in increasing the athletes’ strength. **Graphical Explanation:** There are no graphs or diagrams included in the image, but it presents a table comparing the bench press strength (in unspecified units
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