Question

1647 yes Math 1530 -56 and 1E (4:45pm -7:15pm MW (Spring 1 2018) Homework: Chapter 9 Score: 0 of 1 pt HW Score: 52.59%, 14.73 of 28 pts 9.3.33-T Question Help。 An industrial plant claims to discharge no more than 1000 gallons of wastewater per hour, on the average, into a sample of four hours is selected over a period of a week. The observations are 1738, 1160. 2354, 2762 a. Find the standard error se = □ (Round to two decimal places as needed ) Enter your answer in the answer box and then click Check Ans parts remaining

an industry plant claims to discharge no more than 1000 gallons of wastewater per hour, on the average, into a
neighboring lake. An environmental action group decides to monitor the plant, in case this limit is being exceeded. A random sample of hours is selected over a period of a week. The observation are 1738, 1160, 2354, 2762.

Find the standard error.

To test Ho: u=1000 vs Ha:u>1000, find the test statistic.

Find the p-value.

Answer 1

To find the standard error we need to find the standard deviation of the sample. Following table shows the calculations for standard deviation:

	X	(X-mean)^2
	1738	70490.25
	1160	711492.25
	2354	122850.25
	2762	575322.25
Total	8014	1480155

Sample size: n =4

The mean is

$\bar{x}=\frac{\sum x}{n}=\frac{8014}{4}=2003.5$

The standard deviation is

$s=\sqrt{\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}}=\sqrt{\frac{1480155}{3}}\approx 702.4137$

The standard error is

$se=\frac{s}{\sqrt{n}}=351.21$

The test statistics is

$t=\frac{\bar{x}-\mu}{se}=\frac{2003.5-1000}{351.21}=2.857$

Degree of freedom: df=n-1=3

The p-value is :  0.0324