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Questions and Answers
What is the set of all possible outcomes of an experiment known as?
What is the set of all possible outcomes of an experiment known as?
What is the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes?
What is the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes?
What is the formula for the Complement Rule?
What is the formula for the Complement Rule?
What is the middle value of a dataset when in order known as?
What is the middle value of a dataset when in order known as?
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What is the difference between the largest and smallest values in a dataset?
What is the difference between the largest and smallest values in a dataset?
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What is the square root of the variance?
What is the square root of the variance?
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What is a statement of no effect or difference in hypothesis testing?
What is a statement of no effect or difference in hypothesis testing?
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What is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true?
What is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true?
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What is the maximum amount by which the sample statistic may differ from the population parameter?
What is the maximum amount by which the sample statistic may differ from the population parameter?
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What is the probability that the interval contains the population parameter?
What is the probability that the interval contains the population parameter?
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Study Notes
Probability
Basic Concepts
- Experiment: an action or situation that can produce a set of outcomes
- Outcome: a specific result of an experiment
- Sample Space: the set of all possible outcomes of an experiment
- Event: a set of outcomes of an experiment
Probability Measures
- Probability: a number between 0 and 1 that represents the likelihood of an event occurring
- Theoretical Probability: the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes
- Experimental Probability: the probability of an event occurring based on repeated trials of an experiment
Rules of Probability
- Complement Rule: P(A') = 1 - P(A)
- Addition Rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
- Multiplication Rule: P(A ∩ B) = P(A) * P(B|A)
Statistics
Descriptive Statistics
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Measures of Central Tendency:
- Mean: the average value of a dataset
- Median: the middle value of a dataset when in order
- Mode: the most frequently occurring value in a dataset
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Measures of Variability:
- Range: the difference between the largest and smallest values in a dataset
- Interquartile Range (IQR): the difference between the 75th percentile and the 25th percentile
- Variance: the average of the squared differences from the mean
- Standard Deviation: the square root of the variance
Inferential Statistics
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Hypothesis Testing:
- Null Hypothesis (H0): a statement of no effect or difference
- Alternative Hypothesis (H1): a statement of an effect or difference
- Test Statistic: a value calculated from sample data to determine whether to reject the null hypothesis
- P-Value: the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true
-
Confidence Intervals:
- Margin of Error: the maximum amount by which the sample statistic may differ from the population parameter
- Confidence Level: the probability that the interval contains the population parameter
Probability
Basic Concepts
- An experiment is an action or situation that can produce a set of outcomes
- An outcome is a specific result of an experiment
- A sample space is the set of all possible outcomes of an experiment
- An event is a set of outcomes of an experiment
Probability Measures
- Probability is a number between 0 and 1 that represents the likelihood of an event occurring
- Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of outcomes
- Experimental probability is calculated by repeating an experiment multiple times and finding the frequency of the event
Rules of Probability
- The complement rule states that the probability of an event not occurring is 1 minus the probability of the event occurring
- The addition rule states that the probability of two events occurring is the sum of their individual probabilities minus the probability of their intersection
- The multiplication rule states that the probability of two events occurring together is the product of their individual probabilities, with the second event conditional on the first
Statistics
Descriptive Statistics
- Measures of central tendency describe the middle value of a dataset
- The mean is the average value of a dataset
- The median is the middle value of a dataset when in order
- The mode is the most frequently occurring value in a dataset
- Measures of variability describe the spread of a dataset
- The range is the difference between the largest and smallest values in a dataset
- The interquartile range (IQR) is the difference between the 75th percentile and the 25th percentile
- Variance is the average of the squared differences from the mean
- Standard deviation is the square root of the variance
Inferential Statistics
- Hypothesis testing involves testing a null hypothesis against an alternative hypothesis
- The null hypothesis states that there is no effect or difference
- The alternative hypothesis states that there is an effect or difference
- A test statistic is a value calculated from sample data to determine whether to reject the null hypothesis
- The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true
- Confidence intervals estimate a population parameter based on a sample of data
- The margin of error is the maximum amount by which the sample statistic may differ from the population parameter
- The confidence level is the probability that the interval contains the population parameter
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Description
Learn the fundamental concepts of probability, including experiments, outcomes, sample spaces, and events. Also, explore probability measures like theoretical probability.
