Lecture 10

HFIT-565

Assessment & Evaluation of Health Fitness Parameters

Fall Semester 2008

Dr. Marc Schaeffer

Lecture Notes Class #10

Thursday October 30, 2008

Topics for Discussion

Assignment #9 due (solutions)

Sample problem to introduce the general method of solving intervals about sample proportions
Introduction to Proportion Confidence Intervals CI
Things you should not say about your CI
Dealing with Margin of Error (ME)
introduction to c² (this is in the next lecture)
there is a quiz at the end of our class today (click here to see key)

Brief overview of the page 486 Sea Fan problem

51.9% (54/104) of random sample of sea fans on the Las Redes Reef are infected
do you suppose a second random sample would contain 51.9% infection? Why?
so, what can we say about sea fans at this location based on this 51.9% infection?

Some Important details

if we do NOT know p, we cannot find the true standard deviation sigma
thus, we use phat AND we find the standard error (SE)
how is the SE calculated -- SE = sqrt(pq ÷ n)
in this sea fan problem the SE = 4.9% [sqrt (0.519 * 0.481)/104]
we could go on and say that for phat = 51.9%, that 68% of the sample phats fall within 51.9% ± 4.9% WHY?
also, for phat = 51.9%, that 95% of the sample phats fall within 51.9% ± 2*4.9% WHY?

Four statements we should NOT state about the infected sea fan CI

51.9% of all sea fans on the Las Redes Reef are infected
- we do not have enough information to say this
It is probably true that 51.9% of all sea fans on the Las Redes Reef are infected
- in fact, this is probably NOT true that 51.9% is the true proportion of infected fans
We do not know exactly what proportion of sea fans on the Las Redes Reef are infected, but we know that is within the interval of 51.9% ± 2*4.9%, i.e., 42.1 and 61.7%
- we cannot know for sure that the true proportion is in this range or any particular range
we do not know exactly what proportion of sea fans on the Las Redes Reef are infected, but the interval from 42.1% and 61.7% probably contains the true proportion
- as the book says, this statement is the most defensible of this four but it can be made more accurate with subtle rewording.

Now we get to what you really need to concentrate on

we are 95% confident that between 42.1 and 61.7% of the Las Redes sea fans are infected
- this is good statement representing a confidence interval

Margin of Error (ME)

Assignment #10, Due prior to class 11/6/08

Text Reading & Text Problems

Read De Veaux Chapters 19, 20, 21, 22, 23

Problems Chapter 19: 2, 4, 5, 8, 19, 20, 24, 26