Bio Stat (exam 2) lecture 10 & 11

binomial random variable

Counts how often a particular event occurs in a fixed number of trials

facts of binomial random variable

• fixed number of trials (n)

• the outcome of a trial is either a success or failure (has two outcomes)

• the probability of success is the same for each trial (p)

• trials are independent of one another

the parameters of the binomial distribution

n = number of trials

p = probability of success on each trial

q = probability of failure

x = number of successes

simulation study

A computer experiment that involves creating randomly generated data to understand behavior and the effectiveness of statistical methods

• Relies on assumptions

central limit theorem (CLT)

As the sample size gets larger (n), the sampling distribution of the sample mean becomes approximately normal

• Larger sample size = more normal sampling distribution

• mean of sampling distribution = population mean

sampling distribution of X (sample mean)

the distribution of all possible sample means from repeated random samples of the same size

standard error

The standard deviation of the sampling distribution of the sample mean

• measures how much sample means typically vary from the true population mean

standard error

SE = population standard deviation / square root of n (sample size)

as sample size (n) increase

standard error decreases