PSYC 203 1st Edition Lecture 16Outline of Last Lecture I. ReviewII. Answer Monty hall problemIII. Null hypothesisIV. Alternative hypothesisV. Specifying null and research hypothesisVI. Practice problems Outline of Current Lecture I.Review II.Normal Curve III.Z-scoresIV.AsymptoticCurrent LectureI.Review a. Monty Hall Problem – Switch!!! That’s the right answerb. Attributes of Good Hypothesesi. Declaration, Specific, Based on the Literature, Concise, Testablec. A Null Hypothesis is about the Populationd. A Research Hypothesis is about the samplee. Directional versus Non-Directional Hypothesesi. One also predicts the direction in which the changes will occur, while the other just predicts that changes will occur(non-directional)II.Normal Curve These 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.a.b. 3 defining features– Mean, Median, and Mode are equivalent – Perfectly symmetricalc. Asymptotic• Tails get closer and closer to the x-axis but never touch itd. With big enough samples, the distribution of many variables approximates the shape of a normal curvei. Ex: Heightii. IQe. The normal curve serves as a foundation for determining probability for many statistical tests in 203.f. The odds of any one person being very short or very tall are smalli. If we randomly pick a person from the population, the odds they are of “average” height is higher than the odds they are very short or very tall.1. Reason: More of them!!!g. We can use standard deviations to split this curve into sections.i. For example, this distribution has a standard deviation of 10 and a mean of 100.h.III.Z-scoresa.Determining a raw score from a z-score b. z=(X-x)/s so X=x+z(s)c. Z scores tell you how far a point is from its mean and rely on standard deviations as the metric (a type of standard score)i. i.e. how many standard deviations are you away from the mean?d. z-scores can be directly compared across distributionse. Important because raw scores (x values) don’t give you much information about their position relative to the rest of the distribution.f. A z-score not only tells you where the score falls relative to the mean, but also the probability of getting a score higher/lower than that score!g. This is because we can relate the z-score back to the distribution of the normal curve (in sections)IV.Asymptotica. This is why its important that the normal curve is asymptoticb. There is always some probability of an extreme score c. Though this probability gets smaller and smaller the further you move away fromthe mean d. When a vertical line is drawn through a normal distribution:e. 1. The exact location of the line can be specified by a z- score.f. 2. The line divides the distribution into two sections. The larger section is called the body (B) and the smaller section is called the tail (C).g. Whatproportion ofthenormaldistribution corresponds to z-scores greater than 2.00? – For a normal distribution, what is the probability of selecting a z-score less than 0.50? i. Solve these in steps. h. – Sketch the normal distribution i. – Locate the relevant z-score. Determine whether the question asks for proportions for the body or tail. j. – Estimate body/tail proportion k. Most of the time the z-score isn’t going tobe a whole number (e.g. 1, 2, 3, -1, -2,