Is memory ability before a meal the same as after a meal? Ten people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability. Before a Meal Ho: Select an answer H₁: Select an answer ✓ After a Meal Assume a Normal distribution. What can be concluded at the the a = 0.01 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Score on the Memory Test 67 44 71 77 63 76 53 50 71 82 b. The test statistic ? ✓ 76 54 71 86 75 88 58 49 89 83 Select an answer Select an answer V = Select an answer Select an answer (please enter a decimal) (Please enter a decimal) (please show your answer to 3 decimal places.) c. The p-value = d. The p-value is ? ✓ a e. Based on this, we should [Select an answer the null hypothesis. f. Thus, the final conclusion is that ... (Please show your answer to 4 decimal places.)

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Title: Investigating Memory Ability Before and After Meals

**Study Overview:**
This study explores whether an individual's memory ability differs before and after consuming a meal. Ten participants were assessed with memory tests administered prior to and following a meal. A higher score on the test indicates enhanced memory performance.

**Memory Test Scores:**

|                    | **Before a Meal** | **After a Meal** |
|--------------------|-------------------|------------------|
| **Participant 1**  | 67                | 76               |
| **Participant 2**  | 44                | 54               |
| **Participant 3**  | 71                | 71               |
| **Participant 4**  | 77                | 86               |
| **Participant 5**  | 63                | 75               |
| **Participant 6**  | 76                | 88               |
| **Participant 7**  | 53                | 58               |
| **Participant 8**  | 50                | 49               |
| **Participant 9**  | 71                | 89               |
| **Participant 10** | 82                | 83               |

**Hypothesis Testing:**
Assuming a Normal distribution, the study aims to determine results at the α = 0.01 significance level.

1. **Test Selection:**
   - Choose the appropriate statistical test to analyze the data.

2. **Hypotheses Formulation:**
   - Null Hypothesis (\(H_0\)): Specifies no difference in memory test scores before and after a meal.
   - Alternative Hypothesis (\(H_1\)): Suggests a difference in scores.

3. **Statistical Analysis:**
   - Calculate the test statistic with precision to three decimal points.
   - Determine the p-value, shown to four decimal places for accuracy.

4. **Conclusion:**
   - Compare the p-value with α to accept or reject the null hypothesis.
   - Provide a final conclusion based on the analysis.

Through this study, we aim to enhance understanding of how eating impacts cognitive performance, using quantitative analysis to assess potential differences in memory before and after meals.
Transcribed Image Text:Title: Investigating Memory Ability Before and After Meals **Study Overview:** This study explores whether an individual's memory ability differs before and after consuming a meal. Ten participants were assessed with memory tests administered prior to and following a meal. A higher score on the test indicates enhanced memory performance. **Memory Test Scores:** | | **Before a Meal** | **After a Meal** | |--------------------|-------------------|------------------| | **Participant 1** | 67 | 76 | | **Participant 2** | 44 | 54 | | **Participant 3** | 71 | 71 | | **Participant 4** | 77 | 86 | | **Participant 5** | 63 | 75 | | **Participant 6** | 76 | 88 | | **Participant 7** | 53 | 58 | | **Participant 8** | 50 | 49 | | **Participant 9** | 71 | 89 | | **Participant 10** | 82 | 83 | **Hypothesis Testing:** Assuming a Normal distribution, the study aims to determine results at the α = 0.01 significance level. 1. **Test Selection:** - Choose the appropriate statistical test to analyze the data. 2. **Hypotheses Formulation:** - Null Hypothesis (\(H_0\)): Specifies no difference in memory test scores before and after a meal. - Alternative Hypothesis (\(H_1\)): Suggests a difference in scores. 3. **Statistical Analysis:** - Calculate the test statistic with precision to three decimal points. - Determine the p-value, shown to four decimal places for accuracy. 4. **Conclusion:** - Compare the p-value with α to accept or reject the null hypothesis. - Provide a final conclusion based on the analysis. Through this study, we aim to enhance understanding of how eating impacts cognitive performance, using quantitative analysis to assess potential differences in memory before and after meals.
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