July 17, 2012-Lesson on Confidence Intervals for Proportions, Variances and Standard Deviation with Sir Salmorin

As we walked through the corridors of the second floor of the new math building, one of our classmates rushed through and told us that Mr. Salmorin will take over the class of Ms. Macatigos for our advanced Statistics. I felt like I’ll had a worse day ‘cause I thought that we will have a test in Algebra and chapter test in Physics and now Mr. Salmorin!

Well for some of my classmates who like the way Mr. Salmorin teach us, it’s just okay for them to have him as our teacher but as for me who don’t like him because of my experiences last year, it is a bad thing for me.

Yet, I should have myself used to the way Sir Sal teach us and today I should listen well on our lesson.

Our lesson started with unlocking of some terms:

Proportion-represents a part of a whole. It can be expressed as a fraction, decimal or percentage. 12%=0.12=12/100 or 3/25. Proportion can also represent probabilities.

Symbols used in proportion Notation

 
Where x=number of sample units that possess the characteristics of interest

                n=sample size

Example 1: In a recent survey of 150 households, 54 had central air conditioning. Find p hat and q hat, where p hat, the proportion of the households that have central air conditioning.

To construct a confidence interval about a proportion, one must use the maximum error of estimate, which is E=Z_a/2 x square root of p hat x q hat/n. Confidence intervals about proportions must meet the criteria that n is greater than or equal to 5 and nq is greater than or equal to 5.

Formula for a specific Confidence Interval for a Proportion

Rounding Rule: Round off to three decimal places.

Example 2: A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Hence, one can be 90% confident that the percentage of men who applied is between 9.6% and 14.4%.

                                                              Sample Size for Proportions

Example 3: A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

We also had the discussion about Confidence Intervals for variances and Standard deviation, yet I don’t understand it clearly because our time didn’t allow us to finish our discussion.

 By: Kent Spencer M. Mendez

           III-Gold