Chapter 17 Sampling Distribution Models

Flashcards about sampling distributions.

Sampling Distribution of the Means

The histogram you’d get if you could see all the means from all possible samples.

Sampling Distribution of the Proportions

The histogram you’d get if you could see all the proportions from all possible samples.

Sampling Distribution Model

Allows us to quantify how a sample proportion varies from sample to sample, and how likely it is that we’d observe a sample proportion in any particular interval.

Binomial Probability Model

Used for Bernoulli Trials; Binom(n, p) where n = number of trials and p = probability of success.

Mean (Binomial)

μ = np (number of trials * probability of success)

Standard Deviation (Binomial)

σ = √npq (square root of number of trials * probability of success * probability of failure)

Sampling Distribution Model for a Sample Proportion Conditions

Sampled values are independent and the sample size is large enough.

Mean of Sampling Distribution Model for a Sample Proportion

μ(p̂) = p

Central Limit Theorem

The sampling distribution of any mean becomes nearly Normal as the sample size grows, assuming observations are independent and collected with randomization.

Randomization Condition

Subjects were randomly assigned to treatments (experiment) or simple random sample of the population (survey).

Independence Assumption

The individuals in the sample must be independent of each other.

10% Condition

Sampling more than about 10% of the population may not be reasonable because the remaining individuals are no longer really independent of each other.

Success/Failure Condition

Sample size must be large enough that we expect to see at least 10 successes and at least 10 failures (np ≥ 10 and nq ≥ 10).

Sampling Error

Variability you’d expect to see from one sample to another; better termed sampling variability.