### Monitoring Wastewater Discharge: An Analysis**Context:** Concerned about the initial monitoring data, the environmental action group decides to continue to monitor the plant and try to gather more evidence for their case. A random sample of twenty-eight hours is selected over a period of a week. The observations (gallons of wastewater discharged per hour) are displayed below:| 887 | 1129 | 1095 | 1167 | 1162 | 982 | 1187 | 1068 | 1217 | 1107 ||-----|------|------|------|------|------|------|------|------|------|| 1051| 1146 | 904 | 1006 | 1302 | 1175 | 1187 | 1143 | 1206 | 975 || 1131| 1145 | 1051 | 1091 | 942 | 1164 | 1027 | 1172 | | |**Statistical Analysis Output:** The output of a statistical analysis software on this dataset is shown below:| N | Mean | Std. Dev. ||----|--------|-----------|| 28 | 1100.7 | 100.1 |**Interpretation:** Reading the output, we find that:- **Sample Size** $ n $ = 28- **Sample Mean** $ \bar{x} $ = 1100.7- **Sample Standard Deviation** $ s $ = 100.1From this, we can calculate the standard error:\[ SE = \frac{s}{\sqrt{n}} \]\[ SE = \frac{100.1}{\sqrt{28}} \approx \]This information provides crucial insights into the variability and average discharge rates over the observed period, aiding in assessing the plant's environmental impact. Note that the observed sample mean is greater than 1000 gallons per hour. This could mean that the plant is discharging more wastewater than they promised, or the plant could be in compliance, and the large numbers were due to sampling variability. To see if this is the case, we will test the hypothesis that $ \mu = 1000 $ against the alternative that $ \mu \neq 1000 $ at a significance level of $ \alpha = 0.05 $.- **Calculate the t-score $ t = \frac{\bar{x} - 1000}{SE} = $ \_\_\_\_**- **The degrees of freedom for the t-score is $ n - 1 = $ \_\_\_\_**If we look up the critical value for this problem in the t-table, we would find that it is 2.052.- The magnitude of the t-score is (○ smaller ○ greater) than the critical value. Therefore we should (○ reject ○ fail to reject) the hypothesis that $ \mu = 1000 $.- Therefore the evidence (○ does not ○ does) provide significant reason to believe that the plant is discharging more wastewater on average than they claim to be.

Answered: Image /qna-images/answer/598e95f0-9db1-451f-8909-e74e1d3e02cf.jpg

Answered: Concerned about the initial monitoring…

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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