9. Properties of a confidence interval Suppose the mean of a population is μ = 61. A researcher (who does not know that μ = 61) selects a random sample of size n from this population. Then she constructs an 80% confidence interval of the population mean.The true population mean and the researcher’s 80% confidence interval of the population mean are shown in the following graph. Use the graph to answer the questions that follow.**Graph Explanation:**- **True Population Mean:** This is represented by a solid orange line labeled “True Population Mean,” positioned at the population mean value of μ = 61.- **80% Confidence Interval:** The confidence interval is depicted as a blue horizontal line above the true population mean. It is labeled “80% Confidence Interval of the Population Mean.” This interval represents the range within which the researcher is 80% confident that the true population mean falls. - **Sample Mean:** A star icon labeled “Sample Mean” indicates the mean of the sample data collected by the researcher. Its position relative to the true mean and the confidence interval varies based on the specific sample. **Instructions for Constructing Confidence Intervals**1. **Marking the Sample Mean:** - Use the grey star to mark the mean of the sample. - Ensure the star is placed on the horizontal blue line segment representing the confidence interval.2. **Constructing the Confidence Interval:** - Subtract and add the quantity \( t_{SM} \) to the sample mean to construct the confidence interval. - For this task, \( t_{SM} = \) [input required].3. **Calculating a 90% Confidence Interval:** - Using the same sample, suppose a 90% confidence interval of the population mean is needed.4. **Comparative Analysis:** - **80% vs. 90% Confidence Interval:** - The center of the 90% confidence interval will be [input required] compared to the 80% confidence interval. - The 90% confidence interval will be [input required] compared to the 80% confidence interval.5. **Effect of Sample Size:** - At the same confidence level, analyzing the impact of [input required] in the sample size can yield similar effects on the confidence interval's width as altering the confidence level from 80% to 90%.**Note:**- Inputs required are indicated by blank spaces where you need to insert the appropriate values or descriptions.

Answered: Image /qna-images/answer/6df1cea5-5556-45a4-a71e-2f6236887ca0.jpg

Answered: Suppose the mean of a population is µ =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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9. Properties of a confidence interval

Suppose the mean of a population is μ = 61. A researcher (who does not know that μ = 61) selects a random sample of size n from this population. Then she constructs an 80% confidence interval of the population mean.

The true population mean and the researcher’s 80% confidence interval of the population mean are shown in the following graph. Use the graph to answer the questions that follow.

**Graph Explanation:**

- **True Population Mean:** This is represented by a solid orange line labeled “True Population Mean,” positioned at the population mean value of μ = 61.

- **80% Confidence Interval:** The confidence interval is depicted as a blue horizontal line above the true population mean. It is labeled “80% Confidence Interval of the Population Mean.” This interval represents the range within which the researcher is 80% confident that the true population mean falls.

- **Sample Mean:** A star icon labeled “Sample Mean” indicates the mean of the sample data collected by the researcher. Its position relative to the true mean and the confidence interval varies based on the specific sample.

**Instructions for Constructing Confidence Intervals**

1. **Marking the Sample Mean:**
- Use the grey star to mark the mean of the sample.
- Ensure the star is placed on the horizontal blue line segment representing the confidence interval.

2. **Constructing the Confidence Interval:**
- Subtract and add the quantity \( t_{SM} \) to the sample mean to construct the confidence interval.
- For this task, \( t_{SM} = \) [input required].

3. **Calculating a 90% Confidence Interval:**
- Using the same sample, suppose a 90% confidence interval of the population mean is needed.

4. **Comparative Analysis:**
- **80% vs. 90% Confidence Interval:**
- The center of the 90% confidence interval will be [input required] compared to the 80% confidence interval.
- The 90% confidence interval will be [input required] compared to the 80% confidence interval.

5. **Effect of Sample Size:**
- At the same confidence level, analyzing the impact of [input required] in the sample size can yield similar effects on the confidence interval's width as altering the confidence level from 80% to 90%.

**Note:**
- Inputs required are indicated by blank spaces where you need to insert the appropriate values or descriptions.

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