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

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### 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.
Transcribed Image Text:### 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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