1. Chapter 12: A World of Proportions By: Antionette L. Wilson Annette Small

2. Intro to Proportions You hear about proportions everywhere “50% of dentist patients prefer this brand of toothpaste or 9 out of 10 dentists recommend this brand”, people hear this all the time in advertisements and health reports. Since proportions are used in such a wide range of subjects and activities there is often much time put into accurately calculating these portions of populations.

3. Helpful and necessary assumptions to keep in mind Is this a Simple Random Sample Is the population at least 10x the sample size When testing the H o : P= P o, the sample size (n) is large enough that both np o and n(1 – p p ) are 10 or more. Then for a Confidence Interval, n is so large that both the count of successes np and the count of failures n(1 – p) are 10 or more.

4. One Sample Proportions One must look for the unknown proportion or the success in a population, then p (the successes/the observed) must be calculated. P represents the mean The Standard Deviation of p is p(1-p)/n Z statistic must be calculated by subtracting its mean and dividing by the standard deviation z= p-p/( p(1-p)/n) In large sample where the sample proportion is close to the mean the Standard deviation is replaced by the standard of error of (p) SE= p(1 - p)/n Confidence Interval has the form estimate (+) z*SE estimate ((p)(+)z* (p(1- p)/n)

5. Handy Calculator keystrokes for One Sample Proportions STAT/TESTS/5:1PropZTest/Enter, these keystrokes are used to test the H o. STAT/TESTS/A:1PropZTest/Enter, these strokes are helpful in determining the Confidence Interval

6. Two Sample Proportions This type of proportion test is used when two populations are being used or two treatments are available based on two independent samples The mean of a 2-proportion sample is p 1 – p 2 (P) is equal to the success of both samples/ success of the observed Confidence Interval of a 2-prop test is calculated using this formula (p 1 – p 2 ) (+) z*SE The Standard of Error (SE) (square root of variance) is (insert square root symbol) (p 1 (1 – p 1 )/n 1 ) + (p 2 (1 – p 2 )/n 2 ) Z statistics are calcualted by using z= p 1 – p 2 /(p (1 - p) (1/n 1 + 1/n 2 )

7. Handy Calculator Keystrokes for Two Proportion Tests STAT/TESTS/6:2PropZTest/ Enter, these keystrokes are to test the H o STAT/ TESTS/B:2PropZInt/Enter, these keystrokes are used for calculating the Confidence Interval

8. Conclusion When you are traveling through the magnificent world of proportions keep in mind that there are certain key items that one must be able to recognize. For instance recognize when a problem is in need of a proportion or a comparison of two proportions. Then there is the ability to calculate sample proportions or proportions that estimate parameters of interest from sample counts. Items as such as these could be vital because this determines the type of tests one would use, and in the world of statistics if the wrong test is used then the whole test is a disaster. Disaster is something no one likes to witness even in the world of statistics.