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Lecture 8

by: Debra Tee

Lecture 8 STATS 250

Debra Tee
GPA 3.85

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About this Document

Populations, Samples, Statistical Inference, Confidence Interval Estimation, Hypothesis Testing, Sampling Distributions.
Thomas Venable Jr
Class Notes
populations, Samples, confidence, interval, estimation, Sampling, distribution
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This 3 page Class Notes was uploaded by Debra Tee on Saturday October 8, 2016. The Class Notes belongs to STATS 250 at University of Michigan taught by Thomas Venable Jr in Fall. Since its upload, it has received 3 views. For similar materials see /class/231658/stats-250-university-of-michigan in Statistics at University of Michigan.


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Date Created: 10/08/16
Lecture  8:  Introduction  to  Inference  and   Understanding  Sampling  Distributions     9.1  Parameters,  Statistics,  and  Statistical  Inference     -   Some  distinctions  to  keep  in  mind:   ▯    Population  versus  Sample   ▯     Parameter  versus  Statistic   -   Population:   Parameter,  population  proportion,  population  mean   -   Sample:   Sample  mean,  sample  proportion,  statistic     Statistical  Inference:   -   the  use  of  sample  data  to  make  judgments  or  decisions  about   populations.     Confidence  Interval  Estimation:     -   A  confidence  interval  is  a  range  of  values  that  the  researcher  is  fairly   confident  will  cover  the  true,  unknown  value  of  the  population   parameter.  In  other  words,  we  use  a  confidence  interval  to  estimate   the  value  of  a  population  parameter.     Hypothesis  Testing:     -   Hypothesis  testing  uses  sample  data  to  attempt  to  reject  a  hypothesis   about  the  population.       9.2  From  Curiosity  to  Questions  About  Parameters   -­  The  Big  5  are  the  commonly  used  five  parameters       9.3  Overview  of  Sampling  Distributions     Sampling  distribution  of  a  statistic:   -   The  distribution  of  all  possible  values  of  a  statistic  for  repeated   samples  of  the  same  size  from  a  population  is  called  the  sampling   distribution  of  the  statistic.       9.4  Normal  Approximation  to  the  Binomial  Distribution     If  X  is  a  binomial  random  variable  based  on  n  trials  with  success  probability   p,  and  n  is  large,  then  the  random  variable  X  is  also  approximately  N(np,   ????????(1 − ????))   Conditions:  The  approximation  works  well  when  both  np  and  n(1  –  p)  are   at  least  10.     -   If  n  is  small  (either  np  or  n(1-­p)  less  than  10),  -­  >  use  binomial   distribution  to  work  out  question   -   If  n  is  large,  -­>  use  normal  approximation  OR  related  normal   approximation  for  sample  proportion.       Sampling  Distribution  of  ????:  If  sample  size  n  is  large  enough  (namely   ▯(▯▯▯) np>=10  and  n(1-­p)  >=10),  then  ????  is  approximately  N(p,   )   ▯ Standard  Deviation  of  ????:  sd(????)  =   ▯(▯▯▯) )   ▯ Standard  deviation:  approximately  the  average  distance  of  the  possible  ????   values  for    repeated  samples  of  the  same  size  n,  from  the  true  population   proportion  p.       Standard  Error  of  ????:  se(????)  =     ????(1 − ????)   ???? Standard  error:  estimate  of  the  standard  deviation  of  ????.      


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