Review2-2up - rise above your principles. Thought: To...

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