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Probability, Key Terms, Population - Coggle Diagram
Probability
Research begins with a question about a population, but data comes from a sample. Probability describes how likely different samples are given what is known about the population. This relationship forms the foundation of inferential statistics.
Ex: Marbles in a Jar.
Jar 1: 50 black, 50 white = probability of drawing either color is 50%
Jar 2: 90 black, 10 white = drawing a black marble is very likely
Knowing the population makeup, we can determine the probability of obtaining specific samples.
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Probability is used to predict the type of samples that are likely to be obtained from a population. Thus, probability establishes a connection between samples and populations. Inferential statistics rely on this connection when they use sample data as the basis for making conclusions about populations.
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Frequency Distributions
If you think of the graph as representing the entire population, then different portions of the graph represent different portions of the population. Because probabilities and proportions are equivalent, a particular portion of the graph corresponds to a particular probability in the population. Thus, whenever a population is presented in a frequency distribution graph, it will be possible to represent probabilities as proportions of the graph
Normal Distributions
Symmetrical; because the shape is consistent, probabilities can be found using the unit normal table
Unit Normal Tables
The body always corresponds to the larger part of the distribution whether it is on the right hand or left hand side; the tail is always the smaller section whether it is on the right or left
Because the normal distribution is symmetrical, the proportions on the right-hand side are exactly the same as the corresponding proportions on the left-hand side; to find proportions for negative z-scores, you must look up the corresponding proportions for the positive value of z
Although the z-score values change signs (+ and −) from one side to the other, the proportions are always positive. Thus, column C in the table always lists the proportion in the tail whether it is the right-hand or left-hand tai
The unit normal table lists relationships between z-score locations and proportions in a normal distribution. For any z-score location, you can use the table to look up the corresponding proportions. Similarly, if you know the proportions, you can use the table to find the specific z-score location. Because we have defined probability as equivalent to proportion, you can also use the unit normal table to look up probabilities for normal distributions.
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For a situation in which several different outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes. If the possible outcomes are identified as A, B, C, D, and so on, then 
Example: Drawing Cards
if you are selecting a card from a complete deck, there are 52 possible outcomes. The probability of selecting the king of hearts is p= 1/52. The probability of selecting an ace is p= 4/52 because there are 4 aces in the deck.
Typically, we use proportions to summarize previous observations, and probability is used to predict future, uncertain outcomes.
“What is the probability of selecting a king from a deck of cards?” can be restated as “What proportion of the whole deck consists of kings?” In each case, the answer is ,4/52 or “4 out of 52.”
Probability Values range from 0 to 1; 0 means the event is impossible, 1 means the event is certain; expressed as decimals or percentages
Random Sampling
method used to ensure that each individual in a population has an equal chance of being selected; referred to as simple random sample
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when selecting more than one individual, the probability of selection must remain constant from one election to the next
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Key Terms
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simple random sample
data set obtained using selection process wherein each individual has equal chance of being selected
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