PSYC123 Workbook 2019 - STUDENT V2 (Repaired).docx

Refer to appendix b p616 in jb x µ σ z 31 p x 31 or

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Refer to Appendix B, p.616 in J&B. X µ σ Z 31 P (X < 31) = __________ or __________% 27
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Workbook 2019: Answers V2 Week 5: Sampling Distributions Pre-tutorial questions (answer before tutorial). Read Chapter 7 J&B It is good practice to always do calculations in this order: (See Weeks 5 and beyond). 1. Summarise the relevant parts of the problem - what is it I am being asked to do? 2. State known values - What do you already know from the question. (e.g., do you have a list of scores, or the sample mean, the sample standard deviation, etc.) 3. State the formula - Which formula(s) will solve this question? 4. Calculate the values missing from the formula (e.g., I have the variance but a t-test needs the standard error go back to step 2: state σ 2 , the formula for SE, calculate it, and so on). 5. Answer your question If you strictly follow this procedure then you will avoid most common errors in calculation, you will be faster, your work will be clearer, your brain will grow plump and juicy with self- satisfaction, and you will get more marks from your tutor even if you make a mistake. Methods: 1) What is sampling error? 2) What is the sampling distribution of the mean? 3) What is the central limit theorem? Describe its implications. 28
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Workbook 2019: Answers V2 The Central Limit Theorem (CLT) can be tricky to comprehend at times even with textbook guidance. Have a look at this short 3 and half minute video which explains the CLT (via bunnies and dragons!) rather comprehensively (ctrl + click to follow the link ): 4) What is the law of large numbers? Describe its implications. BONUS QUESTION: If we assume that practically all the things that we normally measure are on some level the average of random processes, then given the above laws what could we hypothesise about most very large samples? 5) What does the Standard Error of the Mean represent? (HINT: the accuracy or deviation of __ __ in predicting __ __ ) Calculations: 6) What is the formula for calculating the Standard Error of the Mean? 29
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Workbook 2019: Answers V2 Week 5: Sampling Distributions Post-tutorial questions (answer after tutorial). Read Chapter 8 of J&B or Chapter 10 GH 7) If we are sampling from a population with μ = 95, σ = 10 what would be the standard error of the mean for the following sample sizes a) N = 100 σ ´ X = σ N = 10 100 = 10 10 = 1.00 b) N = 20 c) N = 48 d) N = 1000 BONUS QUESTIONS: What do you notice as N increases? Would we take larger or smaller samples to get a smaller standard error? 30
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Workbook 2019: Answers V2 8) If we are sampling from a population with μ = 85, σ = 16 what would be the Z scores for the following sample means with the associated sample sizes , i.e., we need to work out the standard error of the mean, σ ´ X a) ´ X = 77 below , N = 64 σ ´ X = σ N = = Z ¿ ´ X μ σ ´ x = ¿ = ¿ p = b) ´ X = 85 above, N = 20, also find the probability using the distribution table.
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