Fill in the correct values. (Round your answers to three decimal places.) The 90% confidence interval for the mean is Ib to Ib.

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**Section (b): Confidence Interval Calculation**

**Objective:** Calculate the 90% confidence interval for the mean.

- **Task:** Fill in the correct values, rounding your answers to three decimal places.

  - 90% confidence interval for the mean is from [_________] lb to [_________] lb.

**Instructions:** Select the correct description(s) of this interval. More than one option may apply.

  - [ ] The interval is found by adding and subtracting a multiple of the mean to the standard error mean.
  - [ ] The interval is found by adding and subtracting a multiple of the standard error mean from the mean.
  - [ ] The mean of the sample is equal to the mean of the population.
  - [ ] There is a 10% chance that the confidence interval does not contain the mean weight of the school.
  - [ ] There is a 10% chance the mean weight of the school is above the larger number in the interval.
  - [ ] There is a 90% chance that the confidence interval contains the mean weight of the school.

**Section (c): Confidence Interval Analysis**

**Objective:** Calculate the 99% confidence interval for the mean.

- **Task:** Fill in the correct values, rounding your answers to three decimal places.

  - There is a 1% chance the mean weight of the school is outside the interval [_________] lb to [_________] lb.
Transcribed Image Text:**Section (b): Confidence Interval Calculation** **Objective:** Calculate the 90% confidence interval for the mean. - **Task:** Fill in the correct values, rounding your answers to three decimal places. - 90% confidence interval for the mean is from [_________] lb to [_________] lb. **Instructions:** Select the correct description(s) of this interval. More than one option may apply. - [ ] The interval is found by adding and subtracting a multiple of the mean to the standard error mean. - [ ] The interval is found by adding and subtracting a multiple of the standard error mean from the mean. - [ ] The mean of the sample is equal to the mean of the population. - [ ] There is a 10% chance that the confidence interval does not contain the mean weight of the school. - [ ] There is a 10% chance the mean weight of the school is above the larger number in the interval. - [ ] There is a 90% chance that the confidence interval contains the mean weight of the school. **Section (c): Confidence Interval Analysis** **Objective:** Calculate the 99% confidence interval for the mean. - **Task:** Fill in the correct values, rounding your answers to three decimal places. - There is a 1% chance the mean weight of the school is outside the interval [_________] lb to [_________] lb.
**Student Weight Analysis**

The weights, in pounds, of 20 students at a local school have been sampled and recorded in the following analysis.

**Histogram and Box Plot:**
- The central histogram represents the distribution of student weights. It shows a concentration of students in the 160-200 pound range, with the tallest bar appearing around 180 pounds.
- The box plot above the histogram indicates the median, quartiles, and potential outliers. The median weight is marked at 176 pounds, with one outlier above 240 pounds.

**Quantiles Table:**
- Maximum weight: 247 pounds
- Upper and lower percentiles provide additional insights: 210.1 (90th percentile), 192.5 (75th percentile or upper quartile), 176 (median), 158.25 (25th percentile or lower quartile), and 138 (minimum weight).

**Summary Statistics:**
- Mean weight: 178.6 pounds
- Standard deviation (Std Dev): 24.690505 
- Standard error of the mean (Std Err Mean): 5.5209648

**Confidence Intervals:**
- 90% Confidence Interval for Mean: 
  - Estimate: 178.6
  - Lower CI: 169.0535
  - Upper CI: 188.1465
- 99% Confidence Interval for Mean: 
  - Estimate: 178.6
  - Lower CI: 162.8049
  - Upper CI: 194.3951

For Std Dev:
- 90% Confidence Interval: Lower CI = 19.60242, Upper CI = 33.83613
- 99% Confidence Interval: Lower CI = 17.32658, Upper CI = 41.1389

**Additional Details:**
- Sample size (N): 20 students
- The data suggests variability in weights, with a tendency towards the mean of 178.6 pounds, depicted through a typical distribution spread shown by the standard deviation and accompanying confidence intervals.
Transcribed Image Text:**Student Weight Analysis** The weights, in pounds, of 20 students at a local school have been sampled and recorded in the following analysis. **Histogram and Box Plot:** - The central histogram represents the distribution of student weights. It shows a concentration of students in the 160-200 pound range, with the tallest bar appearing around 180 pounds. - The box plot above the histogram indicates the median, quartiles, and potential outliers. The median weight is marked at 176 pounds, with one outlier above 240 pounds. **Quantiles Table:** - Maximum weight: 247 pounds - Upper and lower percentiles provide additional insights: 210.1 (90th percentile), 192.5 (75th percentile or upper quartile), 176 (median), 158.25 (25th percentile or lower quartile), and 138 (minimum weight). **Summary Statistics:** - Mean weight: 178.6 pounds - Standard deviation (Std Dev): 24.690505 - Standard error of the mean (Std Err Mean): 5.5209648 **Confidence Intervals:** - 90% Confidence Interval for Mean: - Estimate: 178.6 - Lower CI: 169.0535 - Upper CI: 188.1465 - 99% Confidence Interval for Mean: - Estimate: 178.6 - Lower CI: 162.8049 - Upper CI: 194.3951 For Std Dev: - 90% Confidence Interval: Lower CI = 19.60242, Upper CI = 33.83613 - 99% Confidence Interval: Lower CI = 17.32658, Upper CI = 41.1389 **Additional Details:** - Sample size (N): 20 students - The data suggests variability in weights, with a tendency towards the mean of 178.6 pounds, depicted through a typical distribution spread shown by the standard deviation and accompanying confidence intervals.
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