chapter 6 probability
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Chapter 6 Probability. PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J. Gravetter and Larry B. Wallnau. Chapter 6 Learning Outcomes. Concepts to review. Proportions (Math Review, Appendix A) Fractions Decimals Percentages - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 6Probability
PowerPoint Lecture Slides
Essentials of Statistics for the Behavioral Sciences Seventh Edition
by Frederick J. Gravetter and Larry B. Wallnau
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Chapter 6 Learning Outcomes
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Concepts to review
• Proportions (Math Review, Appendix A)– Fractions– Decimals– Percentages
• Basic algebra (Math Review, Appendix A)
• Upper and lower real limits (Chapters1 & 2)
• z-scores (Chapter 5)
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6.1 Introduction to Probability
• Research begins with a question about an entire population.
• Actual research is conducted using a sample.
• Inferential statistics use sample data to answer questions about the population
• Relationships between samples and populations are defined in terms of probability
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Figure 6.1 Role of probability in inferential statistics
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Definition of Probability
• Several different outcomes are possible
• The probability of any specific outcome is a fraction or proportion of all possible outcomes
outcomespossible of number total
A as classified outcomes of number A ofy probabilit =
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Definition of Random Sample
• Each individual in the population has an equal chance of being selected
• Probabilities must stay constant from one selection to the next if more than one individual is selected
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Probability and Frequency Distributions
• Probability usually involves population of scores that can be displayed in a frequency distribution graph
• Different portions of the graph represent portions of the population
• Proportions and probabilities are equivalent
• A particular portion of the graph corresponds to a particular probability in the population
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Figure 6.2 Population frequency distribution histogram
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Learning Check
• A deck of cards contains 12 royalty cards.If you randomly select a card from the deck, what is the probability of obtaining a royalty card?
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Learning Check - Answer
• A deck of cards contains 12 royalty cards.If you randomly select a card from the deck, what is the probability of obtaining a royalty card?
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Learning Check TF
• Decide if each of the following statements is True or False.
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Answer FF
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6.2 Probability and the Normal Distribution
• Normal distribution is a common shape– Symmetrical– Highest frequency in the middle– Frequencies taper off towards the extremes
• Defined by an equation
• Can be described by the proportions of area contained in each section.
• z-scores are used to identify sections
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Figure 6.3 The Normal Distribution
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Figure 6.4 Normal Distribution with z-scores
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Traits of the normal distribution
• Sections on the left side of the distribution have the same area as corresponding sections on the right
• Because z-scores define the sections, the proportions of area apply to any normal distribution– Regardless of the mean– Regardless of the standard deviation
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Figure 6.5 Distribution for Example 6.2
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The Unit Normal Table
• The proportion for only a few z-scores can be shown graphically
• The complete listing of z-scores and proportions is provided in the unit normal table
• Complete Unit Normal Table is in Appendix B, Table B.1
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Figure 6.6 Portion of the Unit Normal Table
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Probabilities, Proportions, z-Scores
• Unit normal table lists relationships between z-score locations and proportions in a normal distribution.
• If you know the z-score, you can look up the corresponding proportion.
• If you know the proportions, you can use the table to find the specific z-score location.
• Probability is equivalent to proportions.
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Figure 6.7 Distributions for Examples 6.3A to 6.3C
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Figure 6.8 Distributions for Examples 6.4A and 6.4B
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Learning Check
• Find the proportion of the normal curve that corresponds to z > 1.50
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Learning Check - Answer
• Find the proportion of the normal curve that corresponds to z > 1.50
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Learning Check
• Decide if each of the following statements is True or False.
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Answer
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6.3 Probabilities and proportions for scores from a normal distribution
• The Unit Normal Table can only be used with normal-shaped distributions; the shape of the distribution should be verified.
• For normal-shaped distributions– Transform the X values into z-scores– Look up the proportions corresponding to the
z-score values.
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Figure 6.9 Distribution of IQ scores
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Box 6.1 Percentile ranks
• Percentile rank is the percentage of individuals in the distribution who have scores that are less than or equal to the specific score.
• Probability questions can be rephrased as percentile rank questions.
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Figure 6.10 Distribution for Example 6.6
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Figure 6.11 Distribution for Example 6.7
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Figure 6.12 Determining probabilities or proportions for a normal distribution
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Figure 6.13 Distribution of commuting times
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Figure 6.14 Distribution of commuting times
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Learning Check
• Membership in MENSA requires a score of 130 on the Stanford-Binet 5 IQ test, which has μ = 100 and σ = 15. What proportion of the population qualifies for MENSA?
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Learning Check - Answer
• Membership in MENSA requires a score of 130 on the Stanford-Binet 5 IQ test, which has μ = 100 and σ = 15. What proportion of the population qualifies for MENSA?
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Learning Check
• Decide if each of the following statements is True or False.
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Answer
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6.4 Looking ahead to inferential statistics
• Many research situations begin with a population that forms a normal distribution.
• A random sample is selected and receives a treatment, to evaluate the treatment.
• Probability is used to decide whether the treated sample is “noticeably different” from the population.
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