A surgeon would like to know how long it takes, on average, to complete a coronary artery bypass surgery. She samples 24 surgeries and logs the time it takes to complete each one, in hours: 4.8, 4.7, 4.5, 4.8, 5.1, 4.8, 4.5, 4.8, 4.2, 4.9, 4.7, 4.9, 4.6, 4.6, 4.5, 4.9, 4.8, 4.5, 4.9, 4.8, 5.1, 4.7, 4.7, 4.6 Assuming the population standard deviation is a = 0.25, construct a 89% confidence interval for the average time it takes to complete a coronary artery bypass surgery. H= Margin of Error: E = We are 89% confident that the mean amount of time it takes to complete a coronary bypass sugery hours and is between hours.

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**Title: Constructing an 89% Confidence Interval for Coronary Artery Bypass Surgery Time**

A surgeon seeks to determine the average time to complete a coronary artery bypass surgery. She collects data from 24 surgeries, measuring the time in hours as follows:
4.8, 4.7, 4.5, 4.8, 5.1, 4.8, 4.5, 4.8, 4.2, 4.9, 4.7, 4.9, 4.6, 4.6, 4.5, 4.9, 4.8, 4.5, 4.9, 4.8, 5.1, 4.7, 4.7, 4.6

Given a population standard deviation (σ) of 0.25, the task is to construct an 89% confidence interval for the average surgery time.

**Calculations Needed:**

1. **Sample Mean (x̄):** Calculate the mean of the sample data points.

2. **Confidence Level (α/2):** Determine the significance level associated with the 89% confidence interval.

3. **Z-value (zᵦ/₂):** Find the Z-score corresponding to the confidence level.

4. **Margin of Error (E):** Use the formula for the margin of error, E = zᵦ/₂ * (σ/√n), where n is the sample size.

5. **Confidence Interval:** Calculate the range using (x̄ - E) to (x̄ + E).

**Conclusion:**

We are 89% confident that the mean time needed to complete a coronary artery bypass surgery is between [lower limit] hours and [upper limit] hours.

**Additional Resources:**

For further clarification or assistance, please refer to this [forum link].

(Note: The placeholders for calculations should be filled in with the appropriate computations based on the data provided.)
Transcribed Image Text:**Title: Constructing an 89% Confidence Interval for Coronary Artery Bypass Surgery Time** A surgeon seeks to determine the average time to complete a coronary artery bypass surgery. She collects data from 24 surgeries, measuring the time in hours as follows: 4.8, 4.7, 4.5, 4.8, 5.1, 4.8, 4.5, 4.8, 4.2, 4.9, 4.7, 4.9, 4.6, 4.6, 4.5, 4.9, 4.8, 4.5, 4.9, 4.8, 5.1, 4.7, 4.7, 4.6 Given a population standard deviation (σ) of 0.25, the task is to construct an 89% confidence interval for the average surgery time. **Calculations Needed:** 1. **Sample Mean (x̄):** Calculate the mean of the sample data points. 2. **Confidence Level (α/2):** Determine the significance level associated with the 89% confidence interval. 3. **Z-value (zᵦ/₂):** Find the Z-score corresponding to the confidence level. 4. **Margin of Error (E):** Use the formula for the margin of error, E = zᵦ/₂ * (σ/√n), where n is the sample size. 5. **Confidence Interval:** Calculate the range using (x̄ - E) to (x̄ + E). **Conclusion:** We are 89% confident that the mean time needed to complete a coronary artery bypass surgery is between [lower limit] hours and [upper limit] hours. **Additional Resources:** For further clarification or assistance, please refer to this [forum link]. (Note: The placeholders for calculations should be filled in with the appropriate computations based on the data provided.)
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Given,sample size(n)=24population standard deviation(σ)=0.25

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