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Statistics Calculators: www.statssolver.com/ The addition law can be used to calculate the probability of the union of two events. It says that the probability of the union of two events is the sum of their probabilities minus the probability of their intersection. The reason that the intersection is subtracted in the addition law is that when summing the probabilities, the intersection is coun...

Statistics Calculators: www.statssolver.com/ Consider two events A and B. The union of A and B, written AUB, is the event containing all sample points in A or B or both. For example, consider an experiment with five possible outcomes: E1, E2, E3, E4, E5. Suppose A = {E1, E3} and B = {E2, E3, E5}. Then the union of A and B is AUB = {E1, E2, E3, E5}. The intersection of A and B is the event conta...

Statistics Calculators: www.statssolver.com/ Consider an event A. The complement of A, written Ac, is the even containing all sample points that are not in A. For example, consider the experiment of rolling a die. Recall that the sample points (outcomes) in this experiment are 1,2,3,4,5 and 6. Let's define event A as getting an odd number (1, 3, 5). Then the complement of A will be the even num...

Statistics Calculators: www.statssolver.com/ An event is simply a collection of sample points (outcomes). An even can be defined any way that one likes. For example, consider the experiment of selecting a card from a deck of 52 playing cards. The event of getting an Ace is all the sample points corresponding to getting an ace. Since there are four suits in a deck of cards, there will be four sa...

Statistics Calculators: www.statssolver.com/ When assigning probabilities, there are two requirements and three methods. The first requirement is that the probability of each outcome is between zero and one. The second requirement is that the sum of the probabilities of the outcomes is equal to one. The classical method is appropriate when all outcomes are equally likely. The relative frequency...

Statistics Calculators: www.statssolver.com/ The counting rule for permutations is similar to the one for combinations. It can be used to calculate the number of outcomes when an experiment involves selecting n objects from a larger set of N objects, when the order of selection matters. For example, suppose you are selecting 2 objects from a set of 5 objects. If the objects are labeled A, B, C,...

Statistics Calculators: www.statssolver.com/ The counting rule for combinations can be used to calculate the number of outcomes when an experiment involves selecting n objects from a larger set of N objects. For example, suppose you are selecting 2 objects from a set of 5 objects. If the objects are labeled A, B, C, D and E, there are 10 possible ways of doing this: AB, AC, AD, AE, BC, BD, BE, ...

Statistics Calculators: www.statssolver.com/ A multiple-step experiment is several experiments rolled up into a single experiment. We call each of the individual experiment a step in the multiple-step experiment. For example, tossing 2 coins is a multiple-step experiment because it consists of two individual experiments, or steps. The first step is tossing the first coin and the second step is ...

Statistics Calculators: www.statssolver.com/ An experiment, in probability, is any process that generates a set of outcomes. One simple example of an experiment is tossing a coin. This is considered an experiment because it generates two possible outcomes, head and tail. Another example of an experiment is rolling a die. This is an experiment because it generates six possible outcomes, 1 throug...

Statistics Calculators: www.statssolver.com/ Two-tailed tests in the sigma unknown case are similar to the ones in the sigma known case, except for a few differences. The first difference is that the test statistic follows a t distribution with n-1 degrees of freedom, rather than a z distribution. The p-value is still the probability of getting a test statistic as unlikely as or more unlikely t...

Confidence Interval Calculator: www.statssolver.com/confidence-interval.html NOTE: Margin of error should be 1.6 (not 2.6). For confidence intervals of the population mean: σ unknown, the main difference is that instead of using the z distribution, the t distribution is used. The t distribution is a family of probability distributions, with each individual t distribution depending on the degree...

Statistics Calculators: www.statssolver.com/

Statistics Calculators: www.statssolver.com/ The simple linear regression model describes how y is related to x and an error term. The coefficients in the regression model are called parameters and the error term is a random variable. The regression equation describes how the expected value, or mean, of y is related to the dependent variable. If the parameters of the regression equation were kn...

Statistics Calculators: www.statssolver.com/

Hypothesis Testing | Population Mean: σ Unknown | Upper Tail Test

Hypothesis Testing | Population Mean: σ Known | Two-Tailed Test

Hypothesis Testing | Population Mean: σ Known | Lower Tail Test

Type I and Type II Errors

Developing the Null and Alternative Hypotheses

Standard Deviation

Variance

Interquartile Range

Range

Normal Distribution

Selecting a Sample

Confidence Intervals | Population Mean: σ Known

Binomial Distribution

Sampling Distribution of x̅

Sampling Distributions