PSYC 203 1st Edition Lecture 17Outline of Last Lecture I.Review II.Normal Curve III.Z-scoresIV.AsymptoticOutline of CurrentLectureI. Review a. Normal curve properties i. Symmetrical ii. Asymptotic tails b. Z scores c. Table II. Solving problems with normal curve tables a. Problem solving stepsb. Sample problems c. using z scores to determine percentile rank III. Introduce connection to hypothesis testing Current LectureI. Review a. Normal curve properties i. Symmetrical ii. Asymptotic tails 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.b. Z scores i. Z= (X-xbar)/ s so X=xbar + z(s)ii. When a vertical line is drawn through a normal distribution:iii. 1. The exact location of the line can be specified by a z- score.iv. 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).1.2. in other words, draw a vertical line at the point of your z-score andyou can get a better visual of the body and the tail on the curve, which allows you to see where your score lies c. Table i. Use the table to find the area between the mean and the z-scoreii. For example, if your z-score is .1, area is 3.98 II. Solving Problems with normal curve tables a. Problem solving stepsi. Calculate the relevant z-score(s). ii. Sketch the distribution. iii. Determine if the answer is about the Body or Tail. Anticipate the answer. iv. Look up percentage of the curve beneath the z-score(s) in the Table. v. Use the value(s) to compute your answer.b. Sample problemsi. Sam has a Conscientiousness score of 6.10. He will only hire an assistant who is more conscientious than he is. Imagine the population mean is5.54 and the population standard deviation is 1.05. What percentage of the population will meet Sam’s requirement?1. The z-scores are: z= (1.06-5.54)/1.05.53 (19.85%) (area betweenthe mean and the mode)2. Sketch the distribution in the body, just a little past z score 1. 3. 50%-19.85%=30.15 will fit the requirement ii. Sally has a Neuroticism score of 6.05. Sally wants a dating partner who is less neurotic than she is. Imagine the population mean is 4.67 and the population standard deviation is 1.29. What proportion of the population will meet Sally’s dating requirement?1. Z= (6.05-4.67)/1.29=1.07 (35.77%)2. 50-35.77=19.23% will meet her requirement c. using z scores to determine percentile rank i. Area between mean and Z of 1.27 = 39.80ii. Percentile Rank?1. 50 + 39.80 = 89.80thpercentileiii. Thus far, we have converted raw (x) scores to z-scores and z–scores to probabilities or percentile rank... 1. But... 2. As long as we also know the mean and SD for the distribution, we can also use the Z table to find the raw score associated with a certain probability a. i.e. by using the z-table to find a z-score, then using that z-score to solve for x. b. using formula x=xbar+z(s)III. Introduce connection to hypothesis testing a. Probability is the backbone of inferential statistics b. In Null Hypothesis Significance Testing, we calculate the probability of obtaining our data IF the Null Hypothesis was true. c. If the probability (called a p-value) is less likely than a set cutoff, we reject the null hypothesis d. The cutoff is usually