July 10,2012-Lesson on How to Determine the minimum sample size for finding a confidence interval for the mean.

For this day we were given time to finish our assignments that will be passed for Wednesday, but before we got to answer it, Ms. Macatigos gave us a very short lesson.

Our Lesson is How to Determine the minimum sample size for finding a confidence interval for the mean.

The formula for the sample size is derived from the maximum error of estimate formula.

Example:

The college president asks the statistics teacher to estimate the average age of the students at their college. How large a sample is necessary? The statistics teacher would like to be 99% confident that the estimate should be accurate within one year. From a previous study, the standard deviation of the ages is known to be 3 years.

Round up to 60. Therefore, in order to be 99% confident that the estimate is within one year of the true mean age, the teacher needs a sample of at least 60 students.

Every time that we went out of the 4 corners of our room in Advanced Stat., we must be sure that there is a new idea that we had discovered for this day.

by: Kent Spencer Manalo Mendez

III-Gold

July 11, 2012; a brainstorming day

A brainstorming day.....

      Last Wednesday, July 11, seems like a hard day for us,we have many assignments, tests and activities. It was a habit for us to stay a few minutes in the quadrangle to study and make our assignments. And we are busy studying the steps and formula in finding the mean and standard deviation of a sample. 

      And finally Mam Macatigos gave us our test in Statistics about the Confidence Intervals for the mean (σ is known or n is ≥ to 30) the test is just three items, but it takes more than half an hour for us to finish our test. We have started 7: 45 and end up to 8:30. To avoid cheating and copying of answers, Mam Macatigos prepare two sets of test; set A and B, and give alternately in every column. 

      Most of us take much time in finding the mean and standard deviation of a given sample, because Mam gave us 50 samples. Many of my classmates including me do not have a natural display calculator, so we need to square the sample one by one just to find the standard deviation. Honestly, I am slightly confused how to find the value of E in item no.2 because when Mam discussed about that I think that E means error and to find the E, confidence interval is subtracted to 1, so I represent E as 5 and my answer is wrong that's why I got only 13 out of 15. 

      Next time I will listen more carefully when Mam Macatigos is discussing because I misunderstood some of the topics she discussed.   

By: Tito Nuevacobita Jr. 
      III-Gold

July 4, 2012 ; a special day.

                  July 4, 2012 ; a special day. 

• Exactly one month after the opening of classes. One month of struggles, problems, and challenges we have encountered in school. One month of learning new things, new lessons and meeting new friends. 

• Check day for all quizzes, assignments, and exercises.  We have checked our Quiz no. 5 Application of Normal Distribution and our Quiz no. 6 Central Limit Theorem. And I have observed that some of my classmates cannot determine yet where to shade a region of a normal distribution, either left or right.
• Mam Macatigos was about to announce our scores in assignments, quizzes and exercises, and I felt nervous because I feel like I have low scores. And I have these scores; 

Assignment 140/165 ; quite good and I passed. 
Quizzes 80/85 ; quite very good.
Exercises 78/85 ; good. 


As I heard my scores, I gain more determination to study hard and achieve high grade in this subject, in fact I realize that Statistics is not that hard and not my worst subject anymore.Then I realize that Mam Macatigos is quite better than Sr. Salmorin, because Mam gave us hand-outs to study, she prepare a presentation of our lessons and she is not too fast in discussing our lessons. Not just like last year when Sr. Salmorin was teaching us, I cannot understand what he is discussing, that's why I got my lowest grade ever in my life; 86. 


By: Tito Nuevacobita Jr. 
III-Gold
                  


                 
                 

07- 02- 12 or July 2, 2012: What we did on MONDAY...

Tik tok tik tok... Time is running out and as time passes by in the fabrics of space, we III- Gold students didn't want it just to be wasted and so we treasured it and used it not just minute by minute but every second of it.

Some went to school early, as early as 6:30 am, eager as they are to finish to their task and lighten up their burden for the day. Some came late but with their strong determination to finish it before the time ran out, they successfully passed it on time. The III- Gold as a daily routine, had a cooperative learning of answers after the morning assembly which is also  an additional  factor on how we or some of us finished the heavy task at ease.

The task that we passed was about our quiz # 5: The Application of Normal Distribution and an assignment about the Central Limit Theorem.

And when we entered our statistics room of Miss Macatigos one by one, we came in unprepared, for a new quiz awaited us after we checked our past quiz and assignment. The quiz was about Central Limit Theorem which is our past lesson.

Thanks to our scientific calculator and  our pen and also for our individual and some of us who had cooperated with each other we finished the quiz on time. That was all.


Additional Information about  " The Central Limit Theorem"

Central limit theorem or (CLT) says that, given certain conditions, the mean of large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.

The central limit theorem  also explains why many distributions tend to be close to the normal distribution. The key ingredient is that the random variable being observed should be the sum or mean of many independent identically distributed random variables. 

BY: CARL JOEL E. PALMA III- GOLD

July 3, 2011-Lesson on Normal Approximation to the Binomial Distribution

Days with no assignment in Stat seldom happen.

Yet, we should not be so happy ‘cause we should set up our minds ready for our next lesson, moreover assignments still can help us have sharper minds and helps us have better understanding of our lessons.

Our class started with Ms. Macatigos introducing our new lesson:  The Normal Approximation to the Binomial Distribution.

The normal distribution is often used to solve problems that involve the binomial distribution since when n is large (say, 100), the calculations are too difficult to do by hand using the binomial distribution. When p is approximately 0.5 and as n increases, the shape of the binomial distribution become similar to the normal distribution. The larger the n and the close p is to 0.5 the more similar shape of the binomial distribution is to the normal distribution.

However, when p is close to 0 or1 and n is relatively small, the normal approximation is inaccurate.

Remember: Normal approximation should be used only when (n)(p) and (n)(q) are both greater than 5.

For example if p=0.3 and n=10, (0.3)(10)=3, therefore we can’t be able to use the Normal Approximation to the Binomial Distribution in this problem because 3 is less than 5.

Here in this table the Summary of the Normal Approximation to the Binomial Distribution is shown:

These are the formulas for the mean and standard deviation to be used in normal approximation.

mean=np

standard deviation=square root of npq

  The steps for using the normal distribution to approximate the binomial distribution:

1.   Step 1:    Check to see whether the normal approximation can be used.

2.   Step 2:    Find the mean and the standard deviation.

3.   Step 3:    Write the problem in probability notation, using x.

4.   Step 4:    Rewrite the problem by using the correction for continuity correction factor, and show the corresponding area under the normal distribution.

5.    Step 5:   Find the corresponding z values.

6.    Step 6:   Find the solution.

Sample Problem:

If a baseball player’s batting average is 0.32 or 32%, find the probability that the player will get at most 26 hits in 100 times at bat.

Step by step solution for our sample problem.

By: Kent Spencer M. Mendez

                III-Gold

July 5, 2012- It's Quiz Time

      After the flag ceremony, everyone are busy studying and memorizing some important facts about normal approximation just like how to convert the problem to binomial distribution and its steps. But to our great surprise, Ms. Macatigos let us used our handouts and it made us all happy.

       

       But when our teacher gave the test, we discovered that every student has it's own set of test. And that is also a good idea from our teacher to avoid cheating. Just like how our principal remind us about it, our teacher gave us different set of test to avoid asking to our seatmate and to minimize the noise. And it also value the meaning of honesty.    

      

      As we answered the test,  it became more easier for us to decide if the operation is subtraction or addition because of the previous lessons that we discussed. Everyone seems much happier in answering the test than the previous quizzes because in the previous quizzes it is still not clear for us some of the concepts about normal distribution. And that made us feel that we are already great statisticians. But as we go along, I know we will become more greater statisticians with the help of our teacher.

By: Dustin Joshua A. Esquia III-Gold

Random Trivia...

Did you know that......




Sir Ronald Aylmer Fisher is the well known "Father of Statistics", it is because of his  contributions to experimental design, analysis of variance, and likelihood based methods. This great man lived on 1890 to 1962 and was an English statistician, evolutionary biologist, and geneticist.  He was described as "The greatest of Darwin's successors", and the historian of statistics Anders Hald said "Fisher was a genius who almost single-handedly created the foundations for modern statistical science"

                                                       Sir Ronald Alymer Fisher in his youth

His beginnings...

Fisher was born in East Finchley in London, England, with goodly parents namely George and Katie Fisher. His father was a successful fine arts dealer. He had a joyful childhood, having three older sisters, an older brother, and his mother,  who died when Fisher was 14.

Even though  Ronald Fisher had very poor eyesight he was a precocious student, winning the Neeld Medal which is a competitive essay writing in Mathematics at Harrow School at the age of 16. His poor eyesight was not an obstacle for him and he was tutored in mathematics without the aid of paper and pen, which developed his ability to visualize problems in geometrical terms, without contributing to his interest in writing proper derivations of mathematical solutions, especially proofs. He amazed his peers with his ability and skill to conjecture mathematical solutions without justifying his conclusions by showing intermediate steps. He also had a strong interest in biology, and specially, evolution.

In 1909 he won a scholarship to Gonville and Caius College, Cambridge. There he had many friends and were entangled with the heavy intellectual atmosphere. At Cambridge, he learned of the newly rediscovered theory of Mendelian genetics and eugenics, which he saw as a pressing social as well as scientific issue that encompassed both genetics and statistics.

In 1911 he was involved in forming the Cambridge University Eugenics Society with John Maynard Keynes, R.C. Punnett and Horace Darwin which is Charles Darwin's son. Near Fisher's graduation in 1912, Fisher's tutor informed his student him that despite his enormous aptitude and dedication for scientific work and his mathematical potential, his disinclination to show calculations or to prove propositions unfortunately made him unsuited for a career in applied mathematics, which required greater fortitude. His tutor gave him a "luke-warm" recommendation, saying that if Fisher "had stuck to the ropes he would have made a first class mathematician, but he would not."

His book The Genetical Theory of Natural Selection started in 1928 and was published in 1930. It contained a summary of what was already known to the literature. He also explained and proved that larger populations carry more variation so that they have a larger chance of survival. He set forth the foundations of what was to become known as population genetics.

.

BY: CARL JOEL E.  PALMA III- GOLD