DataScience Class 6

Chapter 5

3 types of distributions

1. The population distribution

2. The data distribution

3. The sampling distribution

Population Distribution

Refers to the true distribution of a random variable for a population

• We make assumptions about a population distribution

Data Distribution

Refers to the distribution of observed values from a sample

Sampling Distribution

Is the probability distribution of a sample statistic

• For example, we may be interested in sample distribution of p hat or x bar

• It shows how you would expect a statistic to vary among similar studies

• Under SOME certain circumstances, the sample distribution of a sample statistic follows an approximately normal distribution

Some key sampling distribution conclusions

The sample mean is a continuous random variable, which varies from sample to sample

• Whenever you take samples from population, you will most likely observe a different sample mean (x bar)

• The sample mean is the average of each sample and the sample men itself is a random variable

Sampling Distribution of a Sample Proportion

For a random sample of size n from a population with true population p, the sampling distribution has a sampling proportion

When n is sufficiently large such that

np> 10 and n(1-p)>10

then the sampling distribution of a sample proportion is approximately normal

p^{^} ~ N(P, √

The condition also required that you have a sufficient number of “successes” and “failures”

Central Limit Theorem

Regardless of the shape of the underlying population distribution, as the sample size n increases, the sampling distribution of the sample mean approaches an approximately normal distribution