Does your confidence interval capture 15 pounds? Answer this question in one sentence. If there are 1,000 students completing this assignment, approximately how many of these students will calculate a confidence interval that captures the value of 15?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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  1. Does your confidence interval capture 15 pounds? Answer this question in one sentence.

  2. If there are 1,000 students completing this assignment, approximately how many of these students will calculate a confidence interval that captures the value of 15? Explain your answer in one or two sentences.

**One Sample T Confidence Interval:**

- **μ:** Mean of variable

**95% Confidence Interval Results:**

| Variable         | Sample Mean | Std. Err.  | DF | L. Limit | U. Limit |
|------------------|-------------|------------|----|----------|----------|
| Sample (Weight)  | 14.35375    | 0.69611918 | 7  | 12.70769 | 15.99981 |

**Explanation:**

This table represents the results of a one sample T confidence interval analysis for the weight of a sample. The objective is to estimate the mean weight (μ) of a population based on the sample data.

- **Sample Mean:** The average weight of the sample, calculated to be 14.35375.
- **Std. Err. (Standard Error):** The standard deviation of the sample mean, noted as 0.69611918, reflects the sampling variability.
- **DF (Degrees of Freedom):** The number of independent values, indicated as 7, used in the calculation of the confidence interval.
- **L. Limit (Lower Limit):** The lower bound of the confidence interval is 12.70769.
- **U. Limit (Upper Limit):** The upper bound of the confidence interval is 15.99981.

This interval suggests that we are 95% confident that the true mean weight of the population lies between 12.70769 and 15.99981.
Transcribed Image Text:**One Sample T Confidence Interval:** - **μ:** Mean of variable **95% Confidence Interval Results:** | Variable | Sample Mean | Std. Err. | DF | L. Limit | U. Limit | |------------------|-------------|------------|----|----------|----------| | Sample (Weight) | 14.35375 | 0.69611918 | 7 | 12.70769 | 15.99981 | **Explanation:** This table represents the results of a one sample T confidence interval analysis for the weight of a sample. The objective is to estimate the mean weight (μ) of a population based on the sample data. - **Sample Mean:** The average weight of the sample, calculated to be 14.35375. - **Std. Err. (Standard Error):** The standard deviation of the sample mean, noted as 0.69611918, reflects the sampling variability. - **DF (Degrees of Freedom):** The number of independent values, indicated as 7, used in the calculation of the confidence interval. - **L. Limit (Lower Limit):** The lower bound of the confidence interval is 12.70769. - **U. Limit (Upper Limit):** The upper bound of the confidence interval is 15.99981. This interval suggests that we are 95% confident that the true mean weight of the population lies between 12.70769 and 15.99981.
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