1. The State Court Administrator for the State of Oregon has commissioned a study of two circuit court jurisdictions within the State to examine the effect of administrative rule differences upon litigation processing time. The two jurisdictions of interest are Coos County and Lane County. Samples of ten cases and seven cases, respectively, were selected at random from the Coos County and Lane County court dockets. Files from each of the sampled cases were examined to determine the total elapsed time required for processing each case, from filing to completion. The processing time for each of the sampled cases is given below. Coos County Lane County Case 1234567899 10 Mean Std. Dev. Processing Time (Days) 48 97 103 117 145 151 179 220 257 294 161.1 76.9 Case 1234567 Mean Std. Dev. Processing Time (Days) 109 145 196 273 289 417 505 276.3 143.7 a. (Single-Sample Estimation) Estimate the mean case processing time for Lane County and develop a corresponding 90% confidence interval.

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1. The State Court Administrator for the State of Oregon has commissioned a study of two circuit court jurisdictions within the State to examine the effect of administrative rule differences upon litigation processing time. The two jurisdictions of interest are Coos County and Lane County. Samples of ten cases and seven cases, respectively, were selected at random from the Coos County and Lane County court dockets. Files from each of the sampled cases were examined to determine the total elapsed time required for processing each case, from filing to completion. The processing time for each of the sampled cases is given below.

**Coos County**

| Case | Processing Time (Days) |
|------|------------------------|
| 1    | 48                     |
| 2    | 97                     |
| 3    | 103                    |
| 4    | 117                    |
| 5    | 145                    |
| 6    | 151                    |
| 7    | 179                    |
| 8    | 220                    |
| 9    | 257                    |
| 10   | 294                    |

- Mean: 161.1
- Standard Deviation: 76.9

**Lane County**

| Case | Processing Time (Days) |
|------|------------------------|
| 1    | 109                    |
| 2    | 145                    |
| 3    | 196                    |
| 4    | 273                    |
| 5    | 289                    |
| 6    | 417                    |
| 7    | 505                    |

- Mean: 276.3
- Standard Deviation: 143.7

a. (Single-Sample Estimation) Estimate the mean case processing time for Lane County and develop a corresponding 90% confidence interval.
Transcribed Image Text:1. The State Court Administrator for the State of Oregon has commissioned a study of two circuit court jurisdictions within the State to examine the effect of administrative rule differences upon litigation processing time. The two jurisdictions of interest are Coos County and Lane County. Samples of ten cases and seven cases, respectively, were selected at random from the Coos County and Lane County court dockets. Files from each of the sampled cases were examined to determine the total elapsed time required for processing each case, from filing to completion. The processing time for each of the sampled cases is given below. **Coos County** | Case | Processing Time (Days) | |------|------------------------| | 1 | 48 | | 2 | 97 | | 3 | 103 | | 4 | 117 | | 5 | 145 | | 6 | 151 | | 7 | 179 | | 8 | 220 | | 9 | 257 | | 10 | 294 | - Mean: 161.1 - Standard Deviation: 76.9 **Lane County** | Case | Processing Time (Days) | |------|------------------------| | 1 | 109 | | 2 | 145 | | 3 | 196 | | 4 | 273 | | 5 | 289 | | 6 | 417 | | 7 | 505 | - Mean: 276.3 - Standard Deviation: 143.7 a. (Single-Sample Estimation) Estimate the mean case processing time for Lane County and develop a corresponding 90% confidence interval.
**Small-Sample Estimation and Testing Problem**

**b. (Single-Sample Testing)** 
In studies that preceded the implementation of several recent administrative rule changes in Lane County, the mean case processing time was determined to be 194 days. Is there sufficient evidence to conclude that the mean processing time is now different from 194 days? Perform your test at the α = 0.10 level of significance and report a (approximate using the t-table or compute to high precision using Excel) *p*-value for the test.

**c. (Two-Sample Testing)** 
Is there sufficient evidence based upon the above data to conclude that the average Lane County case processing time is significantly longer than that of Coos County? Perform your test at the α = 0.05 level of significance and report a (approximate using the t-table or compute to high precision using Excel) *p*-value for the test.
Transcribed Image Text:**Small-Sample Estimation and Testing Problem** **b. (Single-Sample Testing)** In studies that preceded the implementation of several recent administrative rule changes in Lane County, the mean case processing time was determined to be 194 days. Is there sufficient evidence to conclude that the mean processing time is now different from 194 days? Perform your test at the α = 0.10 level of significance and report a (approximate using the t-table or compute to high precision using Excel) *p*-value for the test. **c. (Two-Sample Testing)** Is there sufficient evidence based upon the above data to conclude that the average Lane County case processing time is significantly longer than that of Coos County? Perform your test at the α = 0.05 level of significance and report a (approximate using the t-table or compute to high precision using Excel) *p*-value for the test.
Expert Solution
Step 1

Given Information:

Coos County:

Sample size n=10

Sample mean x¯=161.1

Sample standard deviation s=76.9

Lane County:

Sample size n=7

Sample mean x¯=276.3

Sample standard deviation s=143.7

 

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