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Unformatted text preview: 1 Thought: A clear conscience is usually the sign of a bad STA 2023 c B.Presnell & D.Wackerly - Review for Exam II STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 2 Chapter 4 : Discrete Random Variables memory. ¡ Can COUNT the number of distinct values of the ¡ The Binomial Probability Distribution variable. – Some discrete random variables are binomial – NOT ALL – Binomial Experiment p. 179 Thought: Never do card tricks for the people you play 8 ¢4XXX454 2 £ YA9@976)3§U U T ¦ WVDS¥ 8$¢ £ I R0FEQPH 8¢ £ GFEDC ¢BA89@89756)231 0)'%# !¢  4844 £ "(&$ " £ ¦  ¤¢  £ ¦ ©¨§¥ £ – If poker with. number of trials, : (p. 183) for – Mean (p. 185) : – Variance (p. 185) : – Tables : Contain Thought: To succeed in politics, it is often necessary to ..... rise above your principles. 0 2 3 ..... k k+1 n-1 n STA 2023 c B.Presnell & D.Wackerly - Review for Exam II ¡ ¡ Key to finding correct areas (probabilities) : draw q ¡ Possible values are all those associated with one or and , for ¡ Probabilities are areas under “density function”. more line intervals. 2r d§q Chapter 5 : Continuous Random Variables Areas under normal curves between z-scores of 4 in Table IV, p. 809. 2 3 1 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II for pictures Normal Approx. to the Binomial graph of f(x) Distribution Probability of a “success” : is “large” the distribution of can be approximated with a Normal distribution with mean and standard deviation $  £ H4  ¢ £ 0F¢ x €GFE€C ¡ ¢¡ $  x £ H4  ¢ £ 0F¢ yDwGFEDC ¡ If (p. 185)  Sample size : 8 £ ¦ vu¨S¥ is a continuous r.v.,  9eEgDhgp`Sf9VDhp`§i£ ¦ ¥ £ e g  T ¦ ¥ e T  g ¦ ¥ £ e T  T ¦ @EDhba`§f9Edcba`§¥ ¡ Normal distribution is special case. ¡ If b has a binomial distribution ¢ ¡ a s 1 P(a<X<b) bin 4 ta¢¦ Suppose ¡ 5 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 6 ¡ ONLY use continuity correction when really have ¡ Probabilities involving ’s obtained from $   smaller of and and $ larger of table.  q £ ! " ¢ ¤ ¥ ¨ ©§¦8 $0F¢ x   ¨8 F¢ ©§¦h¨ $ 0F¢ x  ¢¡ large enough? ¨ q  F¢  binomial, approximating with normal. ¡ £ T q f¢ DS¥ ¥¡ T¦  q £ ¥¡ f¢  ¦ S¥ ¡ $ 0F¢ x $#F¢ x  ¨ F¢ ©§¦8 5 5 T qET F¢ §¦8  f¡ ¨ ¨ ¥  T ¦ '5 5 Dh£ T S¥ ¤ ¡ Write probabilities for the binomial variable with the ¡ Use “Continuity Correction.”  “=” sign. ¡ The .5’s are called corrections for continuity. 8 R&5 DhT §i $5 Dhg #§¥ % T  ¦ ¥ £ ¦ g  ¦ .5) to get to edge of box in the binomial histogram. ¡ Smallest values of interest gets a little smaller. 7 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II STA 2023 c B.Presnell & D.Wackerly - Review for Exam II Chapter 6: If we plan to take a random sample of size , ' ¡ All statistics have sampling distributions is more Point Estimator (p. 261) ' ' 5. If the population has a normal dist., then so does , . ), then the sampling distribution of  4H ¢ x 54 C¦ 8'  7s 2  6¢ approximately normal, i.e., is large ' ( ¢  4H ¢ x 54 C¦ s '  6. Central Limit Theorem (CLT): (p. 267) If N regardless of the shape of the population. is , Confidence Coefficient (p. 282) ¡ . True for any ¢ N Interval Estimator (p. 282) ¡ i.e., , etc. (p. 254) Chapter 7: ¡ H is called the standard error of .(p. 266) (" for larger sample sizes. , a Sample. ¡ (p. 266), so dist. of concentrated around with a Population. is an unbiased estimator ' C ¢ x 53£ 3H 4 H (" C C £  ¦ 0 (" 32' p1£ )C . (p. 266, 261) ' . So of A Statistic is a meaningful number associated with is called its sampling distribution. A Parameter is a meaningful number associated ¡ ' (p. 255) 4. Chapter 6: is a random variable. 2. Dist. of 3. and standard ¡ 1. H ¢ deviation C from a population with mean I PH C ¡ The largest value of interest gets a little larger (by Confidence Level (p. 282) 8 9 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 10 Confidence Interval for a ¥2 £ ¦2 @5 !  ¤¨ B5¦ ¡ PARAMETER © © ¦ § I q §  ¨ §  ¨ (P. 283) (P. 300) ¡$ ¡  ¢ ¡  ¢ x I  H  q '  – Population Proportion, ¢ x I  q  '   – Population mean,  8 ¢ I  q ¡   ¡$ ¡  ¢ ¢ ¢x ¢ $ # ¢  ¢  £ ¡ C  ¢ NORMALLY distributed. α/2 1−α C ¢x H is “large”, both estimators are approximately α/2 2 Error of Est. I  Q¨ q Error of Est. formula sheet I  q  If Estimator Parameter Standard table q Standard formula sheet standard errors © ¨ ¡ Estimated 8  estimator ...
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This note was uploaded on 12/15/2011 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.

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