PSYCH 210 Lecture 8 Outline of Last Lecture I. Effects of Adding, Subtracting, Multiplying and Dividing ConstantsII. Descriptive Statisticsa. Z-scoresIII. Inferential Statistics Previewa. ProbabilityOutline of Current Lecture I. Continue probabilityII. Probability and z-scoresa. How to use Unit Normal Tablei. Type Iii. Type IIiii. Type IIICurrent LectureI. Determining probability with…a. SFDX f Rel f = f/N = P7 2 2/32 = 0.6256 4 .1255 6 .18754 8 .253 6 .18752 4 .125These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.1 2 .0625N=32i. Calculate Rel f = Relative frequencya. f/Nii. P(2)? = .125iii. P(x<5)? = 20/32 = .625 or add rel f’s from tableb. Histogramsi. Add bars = add areaii. Important Concept1. Probability = area under a curveII. Properties of a normal distributiona. Unimodal and symmetricalb. 50% of scores lie above the mean; 50% belowi. Mean, median and mode all in centerc. Many types of data fit a normal distributionIII. How to use the Unit Normal Tablea. See handouti. Body value is larger of halves, C value is the tail (smaller)ii. D value: area between z-score and mean (regardless of if it is above or below mean)iii. Table works for positive and negative z-scores!1. If negative, find absolute value on table2. Normal distribution curve is a mirror image!b. Type I Problemi. x >> z >> pii. Ex) μ = 50, σ = 10p(x>55)?1. Sketch area we want to finda. Determine whether we want tail or body value1. Tail2. Convert to za. z= (55-50)/10 = 0.503. Look up probability of z-score on tablea. 0.3085i. DO NOT ROUND THESE VALUES!c. Type II Problemi. p >> z >> x1. probability = percentage = proportion = areaii. Ex) What is the raw score associated with the 75th percentile rank?μ = 100, σ = 20Normal Distribution1. Sketcha. Percentage Rank = cumulative percentagei. Shade in left side of distribution2. Look up p in step 1 on tablea. Find corresponding z-scorei. May not be exact1. Pick value closest (do not need to interpolate)b. B-value: 0.7486 = z = +0.673. Convert z to raw scorea. x= μ+ zσx=100 + 0.67(20)x=113.4iii. Ex) What is the raw score associated with 33rd percentile rank?μ = 100, σ = 20, Normal Distribution1. Sketch2. Use C value on tablea. C = 0.3300 = z= -0.44i. Important to remember NEGATIVE SIGN!3. x= 100 + (-.44)(20)x=91.2d. Type IIIi. Add or subtract areas to determine final probability; Begins like Type I or Type II, but must add/subtract at final stepii. Ex) p(45<x<58)?μ = 100, σ = 20, Normal Distribution1. (Start as Type 1): Sketch2. Convert x’s to z’sa. z45= (45-50)/10 = -0.5b. z58= (58-50)/10 = +0.803. Add/Subtract probabilities from the table to determine final areaa. Various optionsi. Body of z45 – Tail of z58ii. Add D scores of z45 and z58iii. Body of z58 – Tail of z45iv. 1-tail z45-tail z58b. (Using last option):i. z(.50) = 0.3085ii. z(0.8) = 0.2119iii. 1 - 0.3085 – 0.2119 =
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