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 equals 3.234 and the sample standard deviation is s = 2.121.

a) Calculate the 95% two-sided prediction interval on the dissolved oxygen concentration for the next stream that will be tested. (rounded to two decimal places)

Answer 1

Answer:

95% confidence interval: (2.241,4.227)

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 3.234

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, σ = 2.121

95% confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$  

Putting the values, we get,  

$t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.05} = \pm 2.093$  

$3.234 \pm 2.093(\dfrac{2.121}{\sqrt{20}} ) = 3.234 \pm 0.993 = (2.241,4.227)$

(2.241, 4.227) is the required confidence interval.