Question

Read the article "Interval Training" by Christine M. Anderson-Cook. Pick an interval type and explain the concept of the interval type through an example.

Answer 1

(a)

Pick an interval type:

A Confidence Interval for the mean

(b)

EXAMPLE:

Suppose we have 40 observations drawn at random from a large Normally Distributed population. Let Significance Level = = 0.05. Let the sample mean = = 121.2. Sample Standard Deviation (s) = 10.6.

A confidence Interval for the Population Mean is given by:

where

n = Sample Size = 40

is a value, the percentage of a t - distribution with degrees of freedom:

n - 1= 40 - 1 = 39

contained in the interval:

From Table, critical values of t = 2.022

Thus 95% Confidence Interval for the mean of the population is given by:

(c) EXPLANATION:

The Confidence Interval is centered at the sample mean () because it is our single best guess of where the population mean () and the new observations are located.The form of the interval ensures the interval is symmetric in width around this point estimate.