Review2 - STA 2023 c B.Presnell& D.Wackerly Review for...

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Unformatted text preview: STA 2023 c B.Presnell & D.Wackerly - Review for Exam II Thought: A clear conscience is usually the sign of a bad memory. Thought: Never do card tricks for the people you play poker with. Thought: To succeed in politics, it is often necessary to rise above your principles. 1 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 2 Chapter 4 : Discrete Random Variables Can COUNT the number of distinct values of the variable. The Binomial Probability Distribution – Some discrete random variables are binomial – NOT ALL – Binomial Experiment p. 179 : (p. 183) ¡!&&&! #! )('''%$" ¢   ¨  & "¡ ¨ § 76 &¨ 43"¡ ¢ 5 ¤ © 21 ¢ 0 © ¡ §© ¤ ¡ ¢ ¨ £ – Tables : Contain © ¢ – Variance (p. 185) : ¢ – Mean (p. 185) : for ¨ £ number of trials, § ¦¤ ¥ – If for & @9'''%$" ¡!888!#! ..... 0 1 2 3 ..... k k+1 n-1 n ¢ 6 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 3 Chapter 5 : Continuous Random Variables Possible values are all those associated with one or more line intervals. Probabilities are areas under “density function”. graph of f(x) P(a<X<b) a b © If Normal distribution is special case. is a continuous r.v., § $ 5 ¡ § $ ¡ ¢ © ¢ ¤ £ © ¢ § ' ¤ ¢ ¡ £ ¢ § $ 5 ¡ © ¢ 5 ¤ £ © 5 ¤ £ ¢ STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 4 Areas under normal curves between z-scores of in Table IV, p. 809. ¡ and , for Key to finding correct areas (probabilities) : draw pictures Normal Approx. to the Binomial Distribution ¨ ! ¡ ¤ ¢ bin § © Suppose © has a binomial distribution ¡ &¨ ¢ (p. 185) ¢ 1 ! "¡ ¨ is “large” the distribution of © ¨ 3"¡ ¢ ¡ 0 If £ can be approximated with a Normal distribution with mean ¢ 1! ¨ ¡ ¢ 0 and standard deviation  3¨ ¡ Probability of a “success” : § ¦¤ ¥ Sample size : STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 5 ¨ "¡ ¢ £ ¤& ¥ 5 £ § ¡ 5 © ¤ £  3¨ ¡ ¨ "¡ £ ¤& ¥ ¦ ¥ £ § ¡ © ¤ ¦ £  3¨ ¡ § ¨ "¡ ¥ £ ©& ¨ "¡ ¢ ## 5 5 ¨¡ 5 # %# ¥ £ ¤& © ¥ § 5 £ § ¨¤ £ ¡ ¨ 3"¡ The .5’s are called corrections for continuity. The largest value of interest gets a little larger (by .5) to get to edge of box in the binomial histogram. Smallest values of interest gets a little smaller. STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 6 ONLY use continuity correction when really have binomial, approximating with normal. ¥ Probabilities involving ’s obtained from table. large enough? and ¨ and  ¨ ¡ ¦ ¡ ¡ smaller of  larger of Write probabilities for the binomial variable with the § ¤ ¥# 5 © 5 ¤ £ ¢ § £ ¢ # © ¢ ¢ £¤ £ Use “Continuity Correction.” & “=” sign. STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 7 Chapter 6: If we plan to take a random sample of size is a random variable. © 2. Dist. of is called its sampling distribution. © 1. , 1 (p. 255) § ©¤ ¢ 0 ¢ ¡ ¢ is an unbiased estimator . (p. 266, 261) is more 1 © 0 £ 1 ¢ 1  is called the standard error of .(p. 266)  for larger sample sizes. ¡ ¡ ¡ concentrated around © (p. 266), so dist. of 0 0  of 4. . So © 3. © 5. If the population has a normal dist., then so does , . £ 1! 0 ¤ ¤ N ¢ © § ¦ ¡ regardless of the shape of the population. ¡ © approximately normal, i.e., is § 1! 0 ), then the sampling distribution of © £ ( is large ¡ ¢ 6. Central Limit Theorem (CLT): (p. 267) If ¡ . True for any ¡ ¤ N § i.e., ¡ deviation and standard 0 from a population with mean , STA 2023 c B.Presnell & D.Wackerly - Review for Exam II Chapter 6: A Parameter is a meaningful number associated , 21 0 with a Population. , etc. (p. 254) A Statistic is a meaningful number associated with a Sample. All statistics have sampling distributions Chapter 7: Point Estimator (p. 261) Interval Estimator (p. 282) Confidence Coefficient (p. 282) Confidence Level (p. 282) 8 STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 9 Estimated Standard Parameter Estimator Standard Error of Est. Error of Est. © 1 ¡ ¡ ¡  3¨ ¨ ¡ ¡ © ¡ ¡ ¢ ¨ ¨ is “large”, both estimators are approximately ¡ NORMALLY distributed. ¡ 0 If STA 2023 c B.Presnell & D.Wackerly - Review for Exam II 10 ¡ Confidence Interval for a § ¡ # ¥ # ¤ PARAMETER ¤ £ ¦ ¤ ¥£ ¢ α/2 ¦ formula sheet table & ¤ ¢ 2¦ £ ¢ ¨ © § ¤ formula sheet standard errors § estimator α/2 1−α  ¨  ¨ 2 2 (P. 283) 0 ¥ – Population mean, §© 1 ¡  ¨ ¡ 2 (P. 300) ¡  ¨ & ¡ ¨ 2 ¡ ¨ ¡  ¨ 2 §© – Population Proportion, § ¡ ¨ ...
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