### Educational Resource: Statistical Analysis in Medical Research**The Effectiveness of a Blood-Pressure Drug: A Case Study**The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 34.6 for a sample size of 359 and a standard deviation of 6.5.**Task: Estimating Drug Impact on Systolic Blood Pressure**Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level).**Instructions:**1. **Determine the Confidence Interval**: To estimate the reduction in systolic blood pressure with 99% confidence, you will need to calculate the confidence interval.2. **Enter Your Answer**: Provide your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).**Formula Reminder**:The confidence interval for the mean is given by:\[ \text{Confidence Interval} = \bar{X} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \]Where:- $ \bar{X} $ is the sample mean.- $ Z $ is the Z-value from the Z-table corresponding to the 99% confidence level.- $ \sigma $ is the sample standard deviation.- $ n $ is the sample size.**How to Calculate**:1. Find the Z-value for a 99% confidence level.2. Calculate the margin of error.3. Apply the margins to determine the lower and upper bounds of the confidence interval.\[ \boxed{} < \mu < \boxed{} \]**Note**:The answer should be obtained without any preliminary rounding.**Visual Aid**:- Unfortunately, there aren't any graphs or diagrams accompanying this text. However, if there were, they would likely illustrate the sample distribution, the confidence interval construction, or a Z-distribution curve highlighting the critical values for the 99% confidence level. Ensure accuracy and review statistical methods for confidence intervals in medical research for the most reliable results.

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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 34.6 for a sample of size 359 and standard deviation 6.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). Answer should be obtained without any preliminary rounding.

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 34.6 for a sample of size 359 and standard deviation 6.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). Answer should be obtained without any preliminary rounding.

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### Educational Resource: Statistical Analysis in Medical Research

**The Effectiveness of a Blood-Pressure Drug: A Case Study**

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 34.6 for a sample size of 359 and a standard deviation of 6.5.

**Task: Estimating Drug Impact on Systolic Blood Pressure**

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level).

**Instructions:**

1. **Determine the Confidence Interval**: To estimate the reduction in systolic blood pressure with 99% confidence, you will need to calculate the confidence interval.
2. **Enter Your Answer**: Provide your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

**Formula Reminder**:
The confidence interval for the mean is given by:

\[ \text{Confidence Interval} = \bar{X} \pm Z \left( \frac{\sigma}{\sqrt{n}} \right) \]

Where:
- $ \bar{X} $ is the sample mean.
- $ Z $ is the Z-value from the Z-table corresponding to the 99% confidence level.
- $ \sigma $ is the sample standard deviation.
- $ n $ is the sample size.

**How to Calculate**:
1. Find the Z-value for a 99% confidence level.
2. Calculate the margin of error.
3. Apply the margins to determine the lower and upper bounds of the confidence interval.

\[ \boxed{} < \mu < \boxed{} \]

**Note**:
The answer should be obtained without any preliminary rounding.

**Visual Aid**:
- Unfortunately, there aren't any graphs or diagrams accompanying this text. However, if there were, they would likely illustrate the sample distribution, the confidence interval construction, or a Z-distribution curve highlighting the critical values for the 99% confidence level.

Ensure accuracy and review statistical methods for confidence intervals in medical research for the most reliable results.

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