Talbert PSYC510_HW5F.docx - PSYC 510 HOMEWORK 5 Z-Scores...

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PSYC 510 H OMEWORK 5 Z-Scores When submitting this file, be sure the filename includes your full name, course and section. Example: HW5_JohnDoe_510B01 Be sure you have reviewed this module/week’s lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Part I: Concepts Questions 1–8 These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. 1 ) To compute the variability of a distribution of scores, we use the standard _________; but to compute the variability of a distribution of means, we use the standard . deviation error 2 ) Define a distribution of means as described in Nolan and Heinzen (2016). Distribution of means is a distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population. Or the means of samples of individual scores. 3 ) Fill in the blank: A z-score can be thought of as the number of standard deviations that a score is from the mean. Page 1 of 11
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PSYC 510 Part I: Questions 4-8 Remember to show work to receive partial credit where applicable. For help working on these problems, refer to the presentation from this module/week on the normal curve and computing z-scores. 4) Calculating z scores from raw scores: If a population has a mean of =50 and a standard deviation of = 2.5, calculate z scores for each of the following raw scores (X) from this population. Show work on the right hand side, put answers on the left in the space provided. 4a) X = 53; Z = 1.2 Work: 53(X) – 50 / 2.5 = 1.2(Z) 4b) X = 49; Z = -0.4 Work: 49(X) – 50 / 2.5 = -0.4(Z) 4c) X = 51; Z = 0.4 Work: 51(X) – 50 / 2.5 = 0.4(Z) 4d) X = 57; Z = 2.8 Work: 57(X) – 50 / 2.5 = 2.8(Z) 5) Calculating raw scores from z scores: If a population has a mean of =50 and a standard deviation of = 2.5, calculate raw scores (X) for each of the following z scores from this population. Show work on the right hand side, put answers on the left in the space provided. 5a) Z = .43; X = 51.1 Work: 0.43(Z) x 2.5 + 50 = 51.1(X) 5b) Z = -2.17; X = 44.6 Work: -2.17(Z) x 2.5 + 50 = 44.575(X) 5c) Z = -1.0; X = 47.5 Work: -1.0(Z) x 2.5 + 50 = 47.5 5d) Z = 1.25; X = 53.1 Work: 1.25(Z) x 2.5 + 50 = 53.125 6) In a normal curve, what percentage of scores falls: 6a) Below the mean? 50% Mean = 50. 50% above and 50% below 6b) Between the mean and +1 standard deviation (SD) above the mean? 84% Work: 34%+34%+14%+2%=84% 6c) Beyond 2 SD’s away from the mean (in the tails) on both sides? 98%(+) 2%(-) Work: 2%+14%+34%+34%=98%(+) 6d) Between the mean and -2 SD’s below the mean? 48% Work: 34% + 14% = 48% 7)
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