Cheat Sheet Stats

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Chapter 3 Standard units tell you how many standard deviations above or below average a data value is standard units = (actual value – average)/SD actual value = average + (SD x standard units). Standard units are denoted by Z. Chapter 8 Complement rule: P(A) = 1 – P(A doesn 't happen) Multiplication rule: P(A and B both happen) = P(A) x P(B given A happened) Q. 5 random components removed one at a time from box containing 5 defective and twenty working. What is chance of selecting all defective: A. 5/25x4/24x3/23x2/22x1/21. Selecting no defective 1 minus chance of selecting all defective or 20/25 x 19/24 x 18/23 x 17/22 x 16/21 = 2/7 or 29% Q. Important data server breaks down 40% of the time, is operational the other 60%, and…show more content…
Q. Certify less than 5% have errors. 10m per entry. How long to est. % of entries having errors using random sample big enough to get MOE less than 2%. A. SE for % = Sqrt ((True %)(100%-True %)/(Size of Sample)) Margin of error = 2% so Standard Error = 1% 1% = Sqrt ((5%)(100%-%%)/(Size of Sample) Size of the Sample = (5%*95%)/(.01^2) Size of the Sample = 475 Samples At 10 minutes each, 475 Samples = 4750 Minutes = 3.3 Days Q. Ave sample size = 20oz. Random sample of 100 boxes, finds ave = 22oz per box, unsusual? A. Yes, this sample average is unusually high, as the Standard Error for the Average is only .2, which means the margin of error is .4. We would reasonably expect (95% confidence) .4 to be the largest distance between the sample average (22) and the population average (20). 2/sqrt (100) = 10 SE 's above the average, which is very unusual. Q. 80% who book show up. 85 room capacity. Makes 100 reservations. Is it likely there will be enough room? A. SE = Square Root of [80 x (100-80) / 100] = 4. Given a margin of error of 8, the number of rooms needed could be between 72 and 88, therefore 85 hotel rooms may not be enough for the people who show up. Chapter 10 Central Limit Theorem: w/ reasonably large sample size you can use the Normal curve to est. the chance a sample average is within some desired number of SEs from pop average. SD = SE of sample average (by SE formula/rule). Confidence Interval: Interpretation: We are 95% confident the
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