Question

An article in the ASCE Journal of Energy Engineering ("Overview of Reservoir Release Improvements at 20 TVA Dams," Vol. 125, April 1999, pp. 1-17) presents data on dissolved oxygen concentration from streams below 20 dams in the Tennessee Valley Authority system. The sample mean from the observations is x = 3.231 and the sample standard deviation is s= 2.129. Assume population is approximately normally distributed. Round your answers to 2 decimal places. (a) Calculate the 95% two-sided confidence interval on the mean oxygen concentration. sus (b) Calculate the 95% two-sided prediction interval on the dissolved oxygen concentration for the next stream that will be tested. sxn +15 (c) Find an interval that will contain 95% of the values of the dissolved oxygen concentration with 99% confidence. )

Answer 1

a)

sample mean 'x̄=		3.231
sample size    n=		20
std deviation s=		2.1290
std error ='sx=s/√n=2.129/√20=		0.4761

for 95% CI; and 19 df, value of t=		2.093		from excel: t.inv(0.975,19)
margin of error E=t*std error    =		0.996
lower bound=sample mean-E =		2.235
Upper bound=sample mean+E =		4.227
from above 95% confidence interval for population mean =(2.23<μ<4.23)

b)

std errror of mean ='sx=s*√(1+1/n)=		2.182
for 95% CI; and 19 df, value of t=		2.093		from excel: t.inv(0.975,19)
margin of error E=t*std error    =		4.57
lower bound=sample mean-E =		-1.335
Upper bound=sample mean+E=		7.797
from above 95% prediction interval for population mean =(-1.34 ,7.80)

c)

for sample size n=20& 95% tolerance level with 99% CI value of k=		3.1680
sample mean                  x̅=		3.231
standard deviation       σ=		2.129
margin of error              E =	k*std deviation	6.745
lower tolerance level     =	sample mean -E                                                =	-3.514
Higher tolerance level   =	sample mean +E                                                =	9.976

95% tolerance interval =(-3.51 , 9.98)