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PROBABILITY

PROBABILITY. INTRODUCTION TO PROBABILITY. We introduce the idea that research studies begin with a general question about an entire population, but actual research is conducted using a sample. POPULATION. SAMPLE. Inferential Statistics. Probability.

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PROBABILITY

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  1. PROBABILITY

  2. INTRODUCTION TO PROBABILITY We introduce the idea that research studies begin with a general question about an entire population, but actual research is conducted using a sample POPULATION SAMPLE Inferential Statistics Probability

  3. THE ROLE OF PROBABILITY IN INFERENTIAL STATISTICS • Probability is used to predict what kind of samples are likely to 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 conclusion about population

  4. PROBABILITY DEFINITION The probability is defined as a fraction or a proportion of all the possible outcome divide by total number of possible outcomes Number of outcome classified as A Probability of A = Total number of possible outcomes

  5. EXAMPLE • If you are selecting a card from a complete deck, there is 52 possible outcomes • The probability of selecting the king of heart? • The probability of selecting an ace? • The probability of selecting red spade? • Tossing dice(s), coin(s) etc.

  6. PROBABILITY andTHE BINOMIAL DISTRIBUTION When a variable is measured on a scale consisting of exactly two categories, the resulting data are called binomial (two names), referring to the two categories on the measurement

  7. PROBABILITY andTHE BINOMIAL DISTRIBUTION • In binomial situations, the researcher often knows the probabilities associated with each of the two categories • With a balanced coin, for example p (head) = p (tails) = ½

  8. PROBABILITY andTHE BINOMIAL DISTRIBUTION • The question of interest is the number of times each category occurs in a series of trials or in a sample individual. • For example: • What is the probability of obtaining 15 head in 20 tosses of a balanced coin? • What is the probability of obtaining more than 40 introverts in a sampling of 50 college freshmen

  9. TOSSING COIN • Number of heads obtained in 2 tosses a coin • p = p (heads) = ½ • p = p (tails) = ½ • We are looking at a sample of n = 2 tosses, and the variable of interest is X = the number of head The binomial distribution showing the probability for the number of heads in 2 coin tosses 0 1 2 Number of heads in 2 coin tosses

  10. TOSSING COIN Number of heads in 3 coin tosses Number of heads in 4 coin tosses

  11. The BINOMIAL EQUATION (p + q)n

  12. LEARNING CHECK • In an examination of 5 true-false problems, what is the probability to answer correct at least 4 items? • In an examination of 5 multiple choices problems with 4 options, what is the probability to answer correct at least 2 items?

  13. PROBABILITY and NORMAL DISTRIBUTION In simpler terms, the normal distribution is symmetrical with a single mode in the middle. The frequency tapers off as you move farther from the middle in either direction σ μ

  14. PROBABILITY and NORMAL DISTRIBUTION Proportion below the curve  B, C, and D area μ X

  15. B and C area X

  16. B and C area X

  17. B, C, and D area B + C = 1 C + D = ½  B – D = ½ μ X

  18. B, C, and D area B + C = 1 C + D = ½  B – D = ½ μ X

  19. The NORMAL DISTRIBUTION following a z-SCORE transformation -2z -1z 0 +1z +2z 34.13% 13.59% 2.28% μ

  20. 34.13% σ = 7 13.59% -2z -1z 0 +1z +2z 2.28% μ = 166 • Assume that the population of Indonesian adult height forms a normal shaped with a mean of μ = 166 cm and σ = 7 cm • p (X) > 180? • p (X) < 159?

  21. 34.13% σ = 7 13.59% -2z -1z 0 +1z +2z 2.28% μ = 166 • Assume that the population of Indonesian adult height forms a normal shaped with a mean of μ = 166 cm and σ = 7 cm • Separates the highest 10%? • Separates the extreme 10% in the tail?

  22. 34.13% σ = 7 13.59% -2z -1z 0 +1z +2z 2.28% μ = 166 • Assume that the population of Indonesian adult height forms a normal shaped with a mean of μ = 166 cm and σ = 7 cm • p (X) 160 - 170? • p (X) 170 - 175?

  23. EXERCISE • From Gravetter’s book page 193 number 2, 4, 6, 8, and 10

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