My Sunday Letter

Please, don't forget to record the time of learning - writing, solving problems, reading the textbook, etc.

Please reply to this letter at least with Hello. In your reply, you may want to attach your Excel file. I will check (in a very friendly manner) your data, and will e-mail you my feedback. Also, you may want to e-mail me your writing assignment 7; however, asking your questions about WA7 in your group discussion board will count for your grade.

_________________________________Understanding the Central Limit Theorem = Understanding Inferential Statistics

– if you select a random sample from a population with mean μ and standard deviation σ,

---the mean

of this random sample will be part of a normal distribution with mean equal to the mean of the population (μ) and standard deviation

= equal to the standard deviation of the population divided by root square of the size of the sample n.

Central Limit Theorem makes the Normal Distribution very special – every random sample is part of a normal distribution, even if the distribution of the population is not normally distributed.

Z-distribution or T-distribution? You probably remember the joke - "What is a T-party with more than 30 people?" In this chapter you will understand why the answer is "a Z-party."

In chapter 7 you will learn a little bit more about Binomial Distribution, I call it yes/no type of distribution.

Binomial distribution is very common – if the variable has only two possible values, called success or failure, than the distribution is called binomial. If for each trial, the probability for success is p, and the probability for failure is q, than we can calculate the number of cases with success and failure.

For example, few days before the election – any candidate can be elected or not elected. If we select a random sample of registered voters, and ask every individual how he/she will vote, we can calculate the probability for success. We use two symbols

We can use normal distribution with mean to evaluate the population probability for success and failure. Binomial distribution is almost like a normal with mean

Each value of binomial distribution is the number of successes out of n-individuals asked the same question – “Will you vote for this candidate____?” Possible answers are yes or no. The total number of "yes" can vary from 0 to n.

The distribution of the probability to have specific number of "yes" answers is presented on the figure below.

I used Excel with an assumption that in each trial the probability for "yes" is p = .3 - 30% "yes", and 70% "no"

Can you see the similarity with a normal distribution with mean equal μ=n*p

This picture is very similar to a normal distribution with mean = n*p, and standard deviation sigma: