Chapter 4:
The Study of Randomness

Probability means relative frequency

The concepts of outcomes, sample space, events

Basic rules: probabilities are always between 0 and 1, total of all probabilties = 1

Random variables (outcomes are numbers)

·        Discrete Random Variable has a finite set of outcomes. Each outcome is assigned a probability. One important situation is equally likely outcomes. For a discrete random variable there are formulas which use the probabilities to calculate the mean and the standard deviation.

·        Continuous Random Variable can take any value in an interval. Probabilities are given by areas under a density curve. Two important types are the normal distribution and the uniform distribution.

The meaning of the Law of Large Numbers

Computing with complements, sums for disjoint events, products for independent events

Making probability distributions (tables) and histograms for discrete random variables

Counting equally likely outcomes to assign probabilities

Using normalcdf

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Chapter 5:
Sampling Distributions

The Binomial Distribution, a special type of discrete random variable:
·        n independent trials with the same probability of success on each trial.
·        This can be used for both count data X and proportions. The two situations have different formulas for mean and standard deviation.

Sampling distribution of sample means:
·        Every sample of a particular size produces a mean. If we take all possible samples of this size, their means form a distribution.
·        If the population is normally distributed, so are the sample means.

The Central Limit Theorem:
·        If n is large enough, the sample means are normally distributed, regardless of the population distribution. This allows us to use z-scores or normalcdf when working with sample statistics.

Using binompdf and binomcdf

Finding mean and standard deviation for both counts and proportions in a binomial distribution

Finding the mean and standard debviation for a sampling distribution. The mean of the sampling distribution equals the mean of the population and the standard deviation of the sampling distribution equals σ/√n.

Using normalcdf

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Confidence intervals:
·        What confidence level means
·        Choosing sample size

Hypothesis testing:
·        Stating null & alternative hypotheses
·        When to use a one-tailed test or a two-tailed test
·        Interpreting Type I and Type II errors

Finding confidence intervals with the calculator

Calculating sample size for a desired confidence

Finding the test statistic (z-value) and the P-value with a calculator

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