What does the Central Limit Theorem say and why is it so important to inferential statistics?
The central limit theorem states that the distribution of the standard z-score converges to the standard normal distribution as n??.
Why would someone want to know whether a sample had more than 30 observations?
The sampling distribution of x � takes more of a bell shape as the random sample size n increases. The more skewed the population distribution, the larger n must be before the shape is close to normal (bell shape). In practice, the sampling distribution i
What is the continuity correction?
A continuity correction factor is used when you use a continuous function to approximate a discrete one. In simple terms, you use it when you want to approximate a binomial with a normal distribution. It's a way to account for the fact that a normal distr
What is a sampling distribution?
It shows all possible values of the sample proportion and how often these sample proportions are expected to occur in random sampling.
What are the basic distinctions between situations in which the binomial, poisson, and hypergeometric distributions apply?
Binomial -
1. There is a fixed number, n, of identical trials.
2. For each trial, there are only two possible outcomes (success/failure).
3. The probability of success, p, remains the same for each trial.
4. The trials are independent of each other.
5. Th
Suppose you have a population with mean (u) and standard deviations (sigma). What can you say about the sampling distribution of the sample mean for samples of size 20?
-For the sampling distribution of a sample proportion, the mean and standard deviation depend on the sample size n and the population proportion p.
-For a random sample of size n from a population with proportion p, the sampling distribution of the sample
What are the three primary distributions we are interested in when dealing with a quantitative random variable and what symbol do we use to indicate the mean and standard deviation of each?
Discrete Random Variable - A discrete random variable X takes a set of separate values (such as 0, 1, 2, ...). Its probability distribution assigns a probability P(x) to each possible value x.
� For each x, the probability P(x) falls between 0 and 1.
� Th
We needed to make sure that np>15 and n(1-p)>15 in order to use the normal distribution in two situations. What are those situations and why do they both involve the same rule?
-The binomial distribution can be approximated well by the normal distribution when n is large enough that the expected number of successes, np, and the expected number of failures, n ( 1 ? p ) , are both at least 15.
-For a random sample of size n from a
Suppose someone tells you that no matter what they do, when they combine the fact that P(A|B) = P(A^B)/P(B) with the rule that P(A^B) always equals P(A) times P(B), they always find events A and B to be independent. Where did they go wrong in their analys
The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ? B). If Events A and B are mutually exclusive, P(A ? B) = 0. SEE NOTES!!!
Suppose you have the following distribution of the random variable X. Sketch on the same diagram the distribution of X_ for samples of 16 observations. Keep in mind that all probability distributions have the same total area under the curve.
SEE NOTES??