**Experimenting with a New Tranquilizer: Data Collection**Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 8 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:| | ||------|-------|| 2.3 | 3 || 2.1 | 2.5 || 2.8 | 2 || 2.5 | 2.8 |**Explanation of Data Collection:**In this scenario, you are collecting the duration for which the tranquilizer remains effective for each patient. This random sample of 8 patients provides a small dataset from which you can begin to draw preliminary conclusions about the general effectiveness of your new tranquilizer. The data can be analyzed using statistical methods to determine trends, averages, and potential outliers in the effectiveness period. **Constructing and Interpreting a Confidence Interval**1. **Conditions for Constructing a Confidence Interval** *Question: What must be true in order to construct a confidence interval in this situation?* - The population must be approximately normal - The sample size must be greater than 30 - The population mean must be known - The population standard deviation must be known2. **Constructing a Confidence Interval** *Task: Construct a 90% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses). Round upper and lower bounds to two decimal places.* _Example Format: (lower bound, upper bound)_3. **Interpreting a Confidence Interval** *Task: Interpret the confidence interval in a complete sentence. Make sure you include units.* _Example: We are 90% confident that the population mean length of time is between [lower bound] and [upper bound] hours._4. **Evaluating a Given Statement Based on Confidence Interval** *Suppose that the company releases a statement that the mean time for all patients is 2 hours.* - Is this possible? - No - Yes - Is it likely? - No - Yes5. **Constructing an Argument Based on Results** *Task: Use the results above and make an argument in favor or against the company's statement. Structure your essay as follows:* 1. Restate the company's claim and whether you agree with it or not. 2. Use the confidence interval to estimate the likelihood of the company's claim being true. 3. Suggest what the company should do.By understanding these steps, students will be able to construct and interpret confidence intervals, evaluate given statements, and make informed arguments based on statistical evidence.

Name: **Experimenting with a New Tranquilizer: Data Collection**Suppose you
Uploaded: 2024-03-20T07:07:12.000Z
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Description: **Experimenting with a New Tranquilizer: Data Collection**Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 8 patients. The period of effectiveness of the tranquilizer

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d. What must be true in order to construct a confidence interval in this situation? O The population must be approximately normal O The sample size must be greater than 30 O The population mean must be known O The population standard deviation must be known e. Construct a 90% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses) Round upper and lower bounds to two decimal places f. Interpret the confidence interval in a complete sentence. Make sure you include units g. Suppose that the company releases a statement that the mean time for all patients is 2 hours. Is this possible? O No O Yes Is it likely? O No O Yes h. Use the results above and make an argument in favor or against the company's statement. Structure your essay as follows: 1. Restate the company's claim and whether you agree with it or not. 2. Use the confidence interval to estimate the likelihood of the company's claim being true. 3. Suggest what the company should do.