An industrial plant claims to discharge no more than 1000 gallons of wastewater
ID: 3053061 • Letter: A
Question
An industrial 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 42 hours is selected over a period of a month. The data are unimodal and roughly symmetric. R 1123, s- 688, and Standard Error 106.161 (a) Using StatCrunch, the p-value (3 decimal places) (b) Are the conditions met to conduct this test? O Yes, because the data are approximately normal O Yes, x-bar is nearly normal because n > 30. Therefore, the Central Limit Theorem can be used Yes, np and n(1-p) are both> 15 O Yes, because the population is approximately normal because n > 30 ONo, np and n(1-p) are not both>15. (c) At alpha 0.05, which of the following is the correct conclusion? Do not reject the null hypothesis. There is evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour. O Do not reject the null hypothesis. There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour. O Reject the null hypothesis. There is sufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour. O Reject the null hypothesis. There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.Explanation / Answer
Ans:
a)
Test statistic:
z=(1123-1000)/(688/sqrt(42))
z=1.159
p-value=P(z>1.159)=0.123
(if t distribution has to be used,0.127)
b)Yes,x-bar is nearly normal,as n>30,Therefore central limit theorm can be used.
c)As,p-value>0.05,do not reject the null hypothesis.There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.