### Confidence Interval Analysis for 12th Grade Students' HeightsA random sample of 25 12th-grade students was selected to study their heights. The following parameters were observed:- **Sample Mean Height**: 167.5 centimeters- **Sample Standard Deviation**: 11.3 centimetersA technology tool is utilized for calculating a confidence interval, which requires the following inputs: sample size, sample mean, and sample standard deviation. The goal is to interpret the confidence interval using these parameters.#### Steps to Follow:1. **View the Technology Output**: - The output displays key statistics and the calculated confidence interval.2. **Parameters from Technology Output**: - Sample Size (N): 25 - Sample Mean: 167.5 cm - Standard Deviation (StDev): 11.300 cm - Standard Error of the Mean (SE Mean): 2.260 cm - 95% Confidence Interval (CI): (162.836, 172.164) cm3. **Interpreting the Confidence Interval**: - Choose the correct interpretation and fill in the blanks: - The true mean height of all 12th-grade students is estimated to be between **162** cm and **172** cm (rounded to the nearest integer).#### Breakdown of Technology Output:- **N**: Number of students in the sample.- **Mean**: Average height of the sample.- **StDev**: Variation of heights in the sample.- **SE Mean**: Standard error, which measures the accuracy of the sample mean.- **95% CI**: Range in which the true population mean is expected to fall, with 95% confidence.Overall, these calculations provide a statistical foundation for estimating the average height of 12th-grade students based on the sample data.

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Arandom sample of 25 12th-grade students was selected. The sample mean height was 167.5 centimeters, and the sample standard deviation was 11.3 centimeters. a. A technology input menu for calculating a confidence interval requires a sample size, a sample mean, and a sample standard deviation. State how you would fill in these numbers b. Using the accompanying technology output, report the confidence interval in a carefully worded sentence. A Click the icon to view the technology output. a. Sample size: Sample mean: Standard deviation: Technology Output (Type integers or decimals. Do not round.) b. Choose the correct interpretation of the confidence interval below and fill in the answer boxes to complete your choice Mean 25 167 5 One-Sample T SE Mean 2 260 V that the N v is between and StDev 11.300 95% CI (162.836, 172.164) (Round to the nearest integer as needed. Use ascending order) Print Done

Arandom sample of 25 12th-grade students was selected. The sample mean height was 167.5 centimeters, and the sample standard deviation was 11.3 centimeters. a. A technology input menu for calculating a confidence interval requires a sample size, a sample mean, and a sample standard deviation. State how you would fill in these numbers b. Using the accompanying technology output, report the confidence interval in a carefully worded sentence. A Click the icon to view the technology output. a. Sample size: Sample mean: Standard deviation: Technology Output (Type integers or decimals. Do not round.) b. Choose the correct interpretation of the confidence interval below and fill in the answer boxes to complete your choice Mean 25 167 5 One-Sample T SE Mean 2 260 V that the N v is between and StDev 11.300 95% CI (162.836, 172.164) (Round to the nearest integer as needed. Use ascending order) Print Done

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Confidence Interval Analysis for 12th Grade Students' Heights

A random sample of 25 12th-grade students was selected to study their heights. The following parameters were observed:

- **Sample Mean Height**: 167.5 centimeters
- **Sample Standard Deviation**: 11.3 centimeters

A technology tool is utilized for calculating a confidence interval, which requires the following inputs: sample size, sample mean, and sample standard deviation. The goal is to interpret the confidence interval using these parameters.

#### Steps to Follow:

1. **View the Technology Output**:
- The output displays key statistics and the calculated confidence interval.

2. **Parameters from Technology Output**:
- Sample Size (N): 25
- Sample Mean: 167.5 cm
- Standard Deviation (StDev): 11.300 cm
- Standard Error of the Mean (SE Mean): 2.260 cm
- 95% Confidence Interval (CI): (162.836, 172.164) cm

3. **Interpreting the Confidence Interval**:
- Choose the correct interpretation and fill in the blanks:
- The true mean height of all 12th-grade students is estimated to be between **162** cm and **172** cm (rounded to the nearest integer).

#### Breakdown of Technology Output:
- **N**: Number of students in the sample.
- **Mean**: Average height of the sample.
- **StDev**: Variation of heights in the sample.
- **SE Mean**: Standard error, which measures the accuracy of the sample mean.
- **95% CI**: Range in which the true population mean is expected to fall, with 95% confidence.

Overall, these calculations provide a statistical foundation for estimating the average height of 12th-grade students based on the sample data.

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