Can you help me fill in the blanks? I am stuck ### SAT Study Course Impact AnalysisA new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. The following data is collected:#### Score Data| Pre-course score | Post-course score ||------------------|-------------------|| 1200 | 1300 || 960 | 920 || 1010 | 1100 || 840 | 880 || 1100 | 1070 || 1250 | 1320 || 860 | 860 || 1330 | 1370 || 790 | 770 || 990 | 1040 || 1110 | 1200 || 740 | 850 |### Hypothesis Testing**a) Null and Alternative Hypotheses**State the null and alternative hypotheses in terms of the appropriate parameter to test the claim that the study course improves students' SAT scores. Use diff = post - pre.- Null Hypothesis ($H_0$): $ \mu_d = 0$ points- Alternative Hypothesis ($H_a$): $ \mu_d \neq 0$ points**b) Level of Significance**The level of significance is $ \alpha = 0.05 $.**c) Test Statistic**To be calculated. It is necessary to round your answer to the nearest hundredth if required.**d) P-value**To be determined. If necessary, round your answer to four decimal places.**e) Decision**The correct decision is to either reject or fail to reject the null hypothesis based on the calculated p-value and the level of significance.#### Detailed Explanation of DataThe table above lists the SAT scores of 12 individuals before and after they took the study course. The difference in scores will be analyzed to determine if there is a statistically significant improvement due to the course. **Next Steps:**1. Calculate the mean difference in scores (`post-course score - pre-course score`).2. Compute the standard deviation of the differences.3. Use the mean difference and standard deviation to calculate the test statistic (often a t-test) and the p-value.4. Compare the p-value with the significance level ($\alpha$) to draw a conclusion about the null hypothesis.This analysis helps ### Statistical Analysis of SAT Study Course EffectivenessThis section presents the statistical analysis and decision-making process regarding the effectiveness of an SAT study course. The following points summarize the steps and conclusions drawn from the analysis:**e) Decision Regarding the Null Hypothesis:**- The correct decision is to **reject** the null hypothesis.**f) Evidence of Score Improvement:**- There is **sufficient** (dropdown selection) evidence that the average score increased after taking the SAT study course.**g) Confidence Interval for Score Improvement:**- We are 95% confident that the average score improved between \[\] and \[\] points. (If necessary, round your answers to the nearest hundredth.)While there are no graphs or diagrams present in this image, the analysis relies on statistical methods to determine whether the SAT study course effectively improves the average scores of participants. The confidence interval provides a range within which we expect the true average improvement to lie, with 95% certainty.To proceed, you can submit your answer by clicking on the "Submit Question" button.---This textual analysis is beneficial for understanding how statistical decisions and interpretations are made in the context of educational interventions, like SAT study programs.

Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

a) State the null and alternative hypotheses in terms of the appropriate parameter to test the claim that the study course improves students' SAT scores. (Use diff = post - pre.) Ho: ud o points Ha: ud o points b) The level of significance is a = 0.05 c) The test statistic is t v oo (If necessary, round your answer to the nearest hundredth.)

a) State the null and alternative hypotheses in terms of the appropriate parameter to test the claim that the study course improves students' SAT scores. (Use diff = post - pre.) Ho: ud o points Ha: ud o points b) The level of significance is a = 0.05 c) The test statistic is t v oo (If necessary, round your answer to the nearest hundredth.)

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Can you help me fill in the blanks? I am stuck

### SAT Study Course Impact Analysis

A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. The following data is collected:

#### Score Data

| Pre-course score | Post-course score |
|------------------|-------------------|
| 1200 | 1300 |
| 960 | 920 |
| 1010 | 1100 |
| 840 | 880 |
| 1100 | 1070 |
| 1250 | 1320 |
| 860 | 860 |
| 1330 | 1370 |
| 790 | 770 |
| 990 | 1040 |
| 1110 | 1200 |
| 740 | 850 |

### Hypothesis Testing

**a) Null and Alternative Hypotheses**

State the null and alternative hypotheses in terms of the appropriate parameter to test the claim that the study course improves students' SAT scores. Use diff = post - pre.
- Null Hypothesis ($H_0$): $ \mu_d = 0$ points
- Alternative Hypothesis ($H_a$): $ \mu_d \neq 0$ points

**b) Level of Significance**

The level of significance is $ \alpha = 0.05 $.

**c) Test Statistic**

To be calculated. It is necessary to round your answer to the nearest hundredth if required.

**d) P-value**

To be determined. If necessary, round your answer to four decimal places.

**e) Decision**

The correct decision is to either reject or fail to reject the null hypothesis based on the calculated p-value and the level of significance.

#### Detailed Explanation of Data

The table above lists the SAT scores of 12 individuals before and after they took the study course. The difference in scores will be analyzed to determine if there is a statistically significant improvement due to the course.

**Next Steps:**
1. Calculate the mean difference in scores (`post-course score - pre-course score`).
2. Compute the standard deviation of the differences.
3. Use the mean difference and standard deviation to calculate the test statistic (often a t-test) and the p-value.
4. Compare the p-value with the significance level ($\alpha$) to draw a conclusion about the null hypothesis.

This analysis helps

### Statistical Analysis of SAT Study Course Effectiveness

This section presents the statistical analysis and decision-making process regarding the effectiveness of an SAT study course. The following points summarize the steps and conclusions drawn from the analysis:

**e) Decision Regarding the Null Hypothesis:**
- The correct decision is to **reject** the null hypothesis.

**f) Evidence of Score Improvement:**
- There is **sufficient** (dropdown selection) evidence that the average score increased after taking the SAT study course.

**g) Confidence Interval for Score Improvement:**
- We are 95% confident that the average score improved between \[\] and \[\] points. (If necessary, round your answers to the nearest hundredth.)

While there are no graphs or diagrams present in this image, the analysis relies on statistical methods to determine whether the SAT study course effectively improves the average scores of participants. The confidence interval provides a range within which we expect the true average improvement to lie, with 95% certainty.

To proceed, you can submit your answer by clicking on the "Submit Question" button.

---

This textual analysis is beneficial for understanding how statistical decisions and interpretations are made in the context of educational interventions, like SAT study programs.

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