Please help me with the question ### Analyzing Time Served by Prisoners in Different Offense Categories#### OverviewPreliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t-procedures satisfied. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months. Our objective is to obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories.#### Data Summary- Fraud Sample Mean ($ \overline{x}_1 $): 12.37 months- Fraud Sample Standard Deviation ($ s_1 $): 4.05 months- Firearms Sample Mean ($ \overline{x}_2 $): 19.32 months- Firearms Sample Standard Deviation ($ s_2 $): 4.42 monthsThe data obtained from the samples are as follows:| | Fraud | Firearms ||----------|--------|----------|| Sample 1 | 15.7 | 15.9 || Sample 2 | 14.3 | 24.9 || Sample 3 | 18.7 | 9.2 || Sample 4 | 12.1 | 17.1 || Sample 5 | 7.9 | 16.1 || Sample 6 | 22.2 | 24.2 || Sample 7 | 11.6 | 8.1 || Sample 8 | 16.3 | 18.3 || Sample 9 | 12.7 | 7.8 || Sample 10| 23.7 | 20.1 |(Note: $ \overline{x}_1 = 12.37 $, $ s_1 = 4.05 $, $ \overline{x}_2 = 19.32 $, and $ s_2 = 4.42 $)#### Confidence Interval CalculationTo compute a 90% confidence interval for the difference between the means ($ \mu_1 - \mu_2 $) of the two groups, you can use the formula for the confidence interval for the difference between two means:\[ CI = (\overline{x}_1 - \overline{x}_2) \pm t \cd

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Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t-procedures satisfied. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months. Obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories. Fraud Firearms 15.7 15.9 14.3 24.9 18.7 9.2 12.1 17.1 7.9 16.1 22.2 24.2 11.6 8.1 16.3 18.3 12.7 7.8 23.7 20.1 (Note: x, = 12.37, s = 4.05, x2 = 19.32, and s, = 4.42.) %3D to The 90% confidence interval is from (Round to three decimal places as needed.) VS

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t-procedures satisfied. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months. Obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories. Fraud Firearms 15.7 15.9 14.3 24.9 18.7 9.2 12.1 17.1 7.9 16.1 22.2 24.2 11.6 8.1 16.3 18.3 12.7 7.8 23.7 20.1 (Note: x, = 12.37, s = 4.05, x2 = 19.32, and s, = 4.42.) %3D to The 90% confidence interval is from (Round to three decimal places as needed.) VS

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Please help me with the question

### Analyzing Time Served by Prisoners in Different Offense Categories

#### Overview

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t-procedures satisfied. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served, in months. Our objective is to obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories.

#### Data Summary

- Fraud Sample Mean ($ \overline{x}_1 $): 12.37 months
- Fraud Sample Standard Deviation ($ s_1 $): 4.05 months
- Firearms Sample Mean ($ \overline{x}_2 $): 19.32 months
- Firearms Sample Standard Deviation ($ s_2 $): 4.42 months

The data obtained from the samples are as follows:

| | Fraud | Firearms |
|----------|--------|----------|
| Sample 1 | 15.7 | 15.9 |
| Sample 2 | 14.3 | 24.9 |
| Sample 3 | 18.7 | 9.2 |
| Sample 4 | 12.1 | 17.1 |
| Sample 5 | 7.9 | 16.1 |
| Sample 6 | 22.2 | 24.2 |
| Sample 7 | 11.6 | 8.1 |
| Sample 8 | 16.3 | 18.3 |
| Sample 9 | 12.7 | 7.8 |
| Sample 10| 23.7 | 20.1 |

(Note: $ \overline{x}_1 = 12.37 $, $ s_1 = 4.05 $, $ \overline{x}_2 = 19.32 $, and $ s_2 = 4.42 $)

#### Confidence Interval Calculation

To compute a 90% confidence interval for the difference between the means ($ \mu_1 - \mu_2 $) of the two groups, you can use the formula for the confidence interval for the difference between two means:

\[ CI = (\overline{x}_1 - \overline{x}_2) \pm t \cd

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