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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 Lane County Case 1 INSAANBOD 2 3 4 5 6 7 8 9 10 Mean Std. Dev. Processing Time (Days) 48 97 103 117 145 151 179 220 257 294 161.1 76.9 Case 1 H234567 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. 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 a = 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 a = 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.

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 1 INSAANBOD 2 3 4 5 6 7 8 9 10 Mean Std. Dev. Processing Time (Days) 48 97 103 117 145 151 179 220 257 294 161.1 76.9 Case 1 H234567 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. 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 a = 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 a = 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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Small-Sample Estimation and Testing Problem** **Table 1: Student's T-Distribution, Upper Tail Critical Values** The table lists critical values for the Student's t-distribution for different degrees of freedom (df) and significance levels (α). These values are used in hypothesis testing, specifically in determining the threshold at which the null hypothesis can be rejected. **Graph Explanation:** - The graph shows a t-distribution curve with a shaded upper tail area, labeled as α. This area represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. **Table Details:** - The first column lists the degrees of freedom (df). It increases from 1 to infinity, representing different sample sizes or subsamples in statistical tests. - The top row represents the significance level (α), ranging from 0.25 to 0.001. These values indicate the probability of making a Type I error, where a true null hypothesis is incorrectly rejected. - Each cell contains the critical value of the t-distribution for a given degree of freedom and significance level. These values are used to compare against the calculated t-statistic from a sample to make decisions about statistical significance. For example, when df = 10 and α = 0.05, the critical value is 1.812. This means that for a 5% significance level and 10 degrees of freedom, the test statistic must exceed 1.812 to reject the null hypothesis. This table is essential for hypothesis testing in statistics, facilitating decisions about whether there's enough evidence to support the alternative hypothesis for small samples.
Transcribed Image Text:**Small-Sample Estimation and Testing Problem** **Table 1: Student's T-Distribution, Upper Tail Critical Values** The table lists critical values for the Student's t-distribution for different degrees of freedom (df) and significance levels (α). These values are used in hypothesis testing, specifically in determining the threshold at which the null hypothesis can be rejected. **Graph Explanation:** - The graph shows a t-distribution curve with a shaded upper tail area, labeled as α. This area represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. **Table Details:** - The first column lists the degrees of freedom (df). It increases from 1 to infinity, representing different sample sizes or subsamples in statistical tests. - The top row represents the significance level (α), ranging from 0.25 to 0.001. These values indicate the probability of making a Type I error, where a true null hypothesis is incorrectly rejected. - Each cell contains the critical value of the t-distribution for a given degree of freedom and significance level. These values are used to compare against the calculated t-statistic from a sample to make decisions about statistical significance. For example, when df = 10 and α = 0.05, the critical value is 1.812. This means that for a 5% significance level and 10 degrees of freedom, the test statistic must exceed 1.812 to reject the null hypothesis. This table is essential for hypothesis testing in statistics, facilitating decisions about whether there's enough evidence to support the alternative hypothesis for small samples.
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 | Processing | Case | Processing | | | Time (Days) | | Time (Days) | | 1 | 48 | 1 | 109 | | 2 | 97 | 2 | 145 | | 3 | 103 | 3 | 196 | | 4 | 117 | 4 | 273 | | 5 | 145 | 5 | 289 | | 6 | 151 | 6 | 417 | | 7 | 179 | 7 | 505 | | 8 | 220 | | | | 9 | 257 | | | | 10 | 294 | | | - Mean: 161.1 (Coos County), 276.3 (Lane County) - Std. Dev.: 76.9 (Coos County), 143.7 (Lane County) a. (Single-Sample Estimation) Estimate the mean case processing time for Lane County and develop a corresponding 90% confidence interval. 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
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 | | Lane County | | |-------------|------------------|-------------|----------------| | Case | Processing | Case | Processing | | | Time (Days) | | Time (Days) | | 1 | 48 | 1 | 109 | | 2 | 97 | 2 | 145 | | 3 | 103 | 3 | 196 | | 4 | 117 | 4 | 273 | | 5 | 145 | 5 | 289 | | 6 | 151 | 6 | 417 | | 7 | 179 | 7 | 505 | | 8 | 220 | | | | 9 | 257 | | | | 10 | 294 | | | - Mean: 161.1 (Coos County), 276.3 (Lane County) - Std. Dev.: 76.9 (Coos County), 143.7 (Lane County) a. (Single-Sample Estimation) Estimate the mean case processing time for Lane County and develop a corresponding 90% confidence interval. 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
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