Question

The EPA limit on the allowable discharge of suspended solids into rivers and streams is 60 milligrams per liter (mg/l) per day. A study of water samples selected from the discharge at a phosphate mine shows that over a long period, the mean daily discharge of suspended solids is 48 mg/l, but day-to-day discharge readings are variable. State inspectors measured the discharge rates of suspended solids for n = 20 days and found s² = 32 (mg/l)². Find a 90% confidence interval for σ². (Round your answers to three decimal places.)

? to ?

Answer 1

Solution :

Given that,

c = 0.90

s = 5.6569

n = 20

At 90% confidence level the is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

/2,df = 0.05,19 = 30.144

and

1- /2,df = 0.95,19 = 10.117

Point estimate = s2 = 32

2L = 2/2,df = 30.144

2R = 21 - /2,df = 10.117

The 90% confidence interval for 2 is,

(n - 1)s2 / 2/2 < 2 < (n - 1)s2 / 21 - /2

( 19 *32) / 30.144 < 2 < ( 19*32 ) / 10.117

20.170 < 2 < 60.097

(20.170 , 60.097)