!"!#$% &$ ' "$ $ #( %%(# ! ')*#$#+%,&$ "' !"#!$%&'(%)*!+,-.)/0(1 )"#)$%"$* $#(- ."$ /% %+&0#(%!.1 2,' 23#4,$4#5"(6 31$&1#(#*4. *#$# !1"$µ =µ ∀ 1 #(# *4 # .*4 !. " &$µ!1"$σ ) µ−=σ ∀ 5"-σ*67*.σ ) ' 7,89%(* .*#$#*. #(-.*$1&$.$ #(' ) +$: */6 .;+$68"$$0 2 #9## : ;!$'<.#("$.'= 1& $14 #(!1$&&$%" -.*' > ? ) @ ; +, ??? ??) ?) ??A ?B? ?B ??? <"#= C#(.*.#":"&$&$) "$&$+,'D%$"EFG& ' )7>0,* +, )7? &$ )7 H C&$ '(703 ),@%* H C&$ ,**, #: *0 &$' 2 5:($11*("&:0#(..' 0 1 2 3 4 5 0.0 0.1 0.2 0.3 0.4 x p(x) Mua sam tren Internet 5-0#(!1$&&$%"-. 0µσ ) &$σ'+"1:.1 %I&%/"!J.&$0, 0%>0%0*,) CI31KL&$*,))(0*(4)/0 CDMN +ILOL+,L,&$ A87)((, 'D% 2 ' 0%>0%0*,) CIDL&$*,))(0*(4)/0 CDMN ++ILPL31KL,OO)OL+,L,&$A87)((,'D%2' 0%>0%0*,) CIQEL&$*,))(0*(4)/0 CDRSG+IDL,&$A87)((,'D%2' D!$*#- #(*%:. +,&$!J.0&$#:*6 : 7>'(703'* .$PQE.'(703'D%2' Row x p(x) KyVong PhuongSai DoLechChuan 1 0 0.003 3.499 1.05400 1.02664 2 1 0.028 3 2 0.132 4 3 0.309 5 4 0.360 6 5 0.168 8#(!1$&.;!$0 2 #9#"$;&% "-"$?)BB @ : ,B*(,/ )"#)$%CD%/B* $1 *(+* ", &$&$'<( .!J.. -"$$/*' < .":. *# !.$1 !.%($%' N *$.00" 1 &$1-%-0" 1*'G$1 89% (* +#**"1,*.1# #(.'G$1 89% (**;% 0E3 + "&#**"1, * $ *.1*6#(%'G$1 %3F C,F89%8**;%0E3+&# "&#**"1,*#( . &+≤ ,T'C! #($ &04N * #)! J.&).&$":' G59%&,- 01 <(!!J.. #&$ ##'K0!.1%:4! J.%-"$ // / H %#.% #-"$#/U G$#$1% -"$$&$*' ("$.":$# ":.%"'>$%!1"$π+,"$ !%-# .'>*"$Pπ'8#(!1$ &.*("$ µ T π &$ "$σ ) Tπ+Pπ,'8"$**( . xnx xnx n xP − − − = )1( )!(! ! )( ππ +$: */6 .;+$H6 N 1$%:# !$.1 0 $#9#!'8..#6V?W!$ ; .10 2 #9#'1; !$%-$%:#&$$0 2 #9##;$$1'8"$!$0 2 #9#' ' = 1 .&$4 #(!1$& %"-' *' > %- ! ! $ $ 0 2 # 9# "$ * X K$ %- @ ! $ 0 2 #9#X ' >%-:/*6!$0 2 #9#X ' G4"!$ %- #(./*6 "$?';' <"#=N !$ #."$"$0/!0 2 #9#+Y!.7.1#,'! $0 2 #9#"$*(&T ;&$ π T?V'8#(-."$$?%;!$' ' N .*.'#(-."$+?U ;,%&$"$IL' 0%>),//0*3'(*)/*,>,-0 ),//0*3 C;&$-/),I*)0(6&$?'V&$),//0*3,I(%%((6 &$7*%,0-'D%2' Probability Density Function Binomial with n = 5 and p = 0.700000 x P( X = x ) 0.00 0.0024 1.00 0.0284 2.00 0.1323 3.00 0.3087 4.00 0.3602 5.00 0.1681 5-1#6$ $1&&0# B KT;&$ π T?V Z31$&µTπT; Z5"- σ T[ π +P π ,\ ]) T?)@V #(!1$&&$%"-#:*6&#(!1$& &$%"-.&0' *'G$ # 1 #6 %- ! !$$0 2 #9#"$???)@H&$ %-@!$0 2 #9#"$?B?)' ' 5-4 %$!$#."0 2 # 9#:"1#6N *Y00" 1 .*.1*6#($%%' 5-0+≥,1#6+≥,T^+≤),'C&1. 0+ ≤ ),#' 0%>),//0*3'(*)/*,>,-0 -0*4 7),//0*3 C;&$ -/),I*)0(6 &$?'V&$ ),//0*3,I(%%((6 C)&$ 7*%,(** 'D% 2 ' Cumulative Distribution Function Binomial with n = 5 and p = 0.700000 x P( X <= x ) 2.00 0.1631 8#(?B"$0" 1&≤)'%-$ !$#." 0 2 #9#"$+ ≥ ,T^+ ≤ ),T^ ?BT?BA' '5-4 #( &%-#(. /*6 "$?;.$11-%-0 " 1_"$4 ? + ≤ ,T?;' 0%>),//0*3'(*)/*,>,-0 4)(%-0*47),//0*3 C;&$-/),I*)0(6&$?'V&$),//0*3,I(%%((6 C?';&$7*%,(**'D%2' V Inverse Cumulative Distribution Function Binomial with n = 5 and p = 0.700000 x P( X <= x ) x P( X <= x ) 3 0.4718 4 0.8319 N **!J.0" 1.*6&$@'G#%#( T0" 1:*6?;'C&1!!$0 2 #9#*640" 1*6?;'+ ? T, ,((, * 0#$.": . *# !.$%(/# %&(%(.%"$!'` # $.*&G#K 10*( .# "0.% 1# # "%. ..U *Y 1"$!1$&µ": #*4. *#!.%(' .*$1σ ) 0*6µ'8"$* *. x! e p(x) x µ µ − = +$: */6 .;+$6G# $"!& %$ *&$%$2%-*%$".2%$! : $$'G#*4 $1?$'Q#!& $1%:(!!$#*-'Q "#J! *#*4!&$1! !$"$;;]7 '8..]7 !1"$ *'= 14 ' 8#(#*4&$%"-.' *' &$0" 1 ]7 'K %' ' >%-!&%Y.1# 1 %- : "$ * ! !!$' <"#=6 '8#(#*4&$%"-. σ ) T µ T;; σT)@;) *'&$0" 1 5-0%:##(.'K4 #(.!-"$ #( ##(.$? %":%"-+σ,&#(#*4'C_"$ #($?%;&$&$%/"$IL' !"#$ 0%>: J**)+'*>-70*,I- /)( CIL&$*,)7**)++* CK),-I)(*406?&$,0(*406;D%2' %&" "' 0%>),//0*3'(*)/*,(>,((, C&$),//0*3 C;';&$: &$7*%,0- CI+,L&$7*,0(*,)'D%2' %&" "(' 0%>),//0*3'(*)/*,(>,((, C&$ -0*47),//0*3 C;';&$: &$7*%,0- CI +,L&$7*,0(*,)'D%2' ) : 7>'(703'* +,&$ +,&$'(703'D%2' A Data Display Row x p(x) cum p(x) 1 0 0.004087 0.004087 2 1 0.022477 0.026564 3 2 0.061812 0.088376 4 3 0.113323 0.201699 5 4 0.155819 0.357518 6 5 0.171401 0.528919 7 6 0.157117 0.686036 8 7 0.123449 0.809485 9 8 0.084871 0.894357 10 9 0.051866 0.946223 11 10 0.028526 0.974749 12 11 0.014263 0.989012 13 12 0.006537 0.995549 14 13 0.002766 0.998315 15 14 0.001087 0.999401 16 15 0.000398 0.999800 *(%&" " )7>0,* +,&$)7?&$&$)7 C&$'(703),@%*H C &$ ,**,' C &$ *0 #: % &$'D%2' 5:($11*"&:*.' 0 5 10 15 0.00 0.05 0.10 0.15 x p(x) A? ' >%-Y.1#1??)BB >%-.1#:"$?)?)V +-$$10" 1%-0&0 )#, H < $%&,*,(!+,- .)/0(1 0 *$%"$* $#(- ."$"/!% %+&0-. ,' , ,F&,)- 0'(*)/*,1 * - "$ # * J # # !'*-4+%,&$% %J) #(!1$& µ &$%"- σ '* *--"$#". %*-$ #19#$$ 0 U =$ % .**- 2 2 2 )( 2 2 1 )( σ µ πσ − − = x exf <*--%1-$* *-%&(+--,!1"$a µ T? &$σT' 1-%-aT+Pµ,]σH"$#(.* *-' bc_.#(a!..#(J&!1$& µ 0%&(%"- σ ' +$: */6 .;+$L6G$#*4"$ *$. & *-&µT;?&$σT;' [...]... ViTri > Two-Sample T-Test and CI: HPrice, ViTri Two-sample T for HPrice ViTri BacMy NamMy N 23 14 Mean 122498 14 932 7 StDev 37 196 46814 SE Mean 7756 12512 Difference = mu (BacMy) - mu (NamMy) Estimate for difference: -2 6829 90% CI for difference: (-5 033 0, -3 32 9) T-Test of difference = 0 (vs not =): T-Value = -1 . 93 0.062 DF = 35 Both use Pooled StDev = 41 032 ! " #E ? '@ 6 * H, % % # ,0 P-Value = 6 ;... )???' & * 1 " - $ $ "1 : J % :! $ % XN "$ "1 % )% / 0 N "1 "$ ' G : N *% $ "1 1& ' "$ 7 " $ + $ 1 , : 2 * !0 D" " 5E $ )?? # # 7 $ T; d" ' = 6 8 9 0 >! % C C 9 %# 1$ + ,- ' * > - 70 K) ,- ,0 - ( ; & $ - 70 ),P ( I ) ,- % - & 6 ,0 (1 D" " # ,0 - (6 I N L& $ * ( - 70 ,) D % 2' A 8 9 0 >! % C C 8 9 0 >! % C C 9 %: 1$ + ,- ' * > - 70 K) ,- ,0 - ( ) ,- % - & 6 ,0 (1 ; & $ - 70 ),P ( I D" " # ,0 - (6 ,) I N... & )6 σ =σ ' α 3 % B' # (µ 6 ± 9% * ,- ( B' *& ( E D & ) ( ( B' ( B B* µ % 3 # ' ,* − C - E & E 6 H Q ; ( * C ,* " (& ) ( ( 1A < " " $ # &' % &' () ' $ %B < '/ ( ( & C µ & ) BC B ( 6 HB ,9= D ' =3 23 =3 75 2J ( ( * %- σ 1 3 $ @ C , < ' SE* * T * 6Q T % ; % ( & )3, # " =3 =3 23 5 23 & >5 75 =5 23 # 8E % F < & 3 , >2 * 6 ( A One-Sample Z: C1 The assumed sigma = 0.2... 3 '(* ' >2J 6 ,9= D P0 6 * % < 1< * % $ @ 'E ' E* ) * B & ' C ≥2 H I ;≥ 2 & ) * % % '& ) ( π -1 3 , 2 # * * B (B ( 85 K ' < & < & ' 3 ' >2 - & & Test and CI for One Proportion Test of p = 0.5 vs p not = 0.5 Sample 1 ! *& & ' C X 21 N 120 6 Sample p 0.175000 95.0% CI (0.107017, 0.2429 83) ( '(6 * 6 3 72 9 ( >2J Z-Value -7 .12 @ 'B Z P-Value 0.000 * B # %- '(* 6 4 * B & ' C B ( H 3 3 3 - 70 K) ,- ,0 - ( ) ,- % - & 6 ,0 (1 ; & $ - 70 ),P ( I D" " # ,0 - (6 ,) I N L& $ * ( - 70 D % 2' 8 9# 0 > % 0 0* % ,) C I 31 K &$ N + N L& $ * ) ( 0( ,) * 7) , & $ A8 (( , ' D 6 % 2' 6 % 2' 8 9: 0 > % 0 0* % ,) C I 31 K &$ N + N )L& $ * ) ( 0( ,) * 7) ), & $ A8 (( , ' D 8 9+ 0 > % 0 0* % ,) C I 31 K &$ N + N ) : L& $ * ) ( 0( 6 ,) *... (-5 20, 684) T-Test of difference = 0 (vs not =): T-Value = 0 .38 DF = 22 Both use Pooled StDev = 5 23 9 ' ' B E * ,* % 3 " ' B * B' " * & * B'@ 6 '6 * `a ; P-Value = 0.705 > J 6 >>J E ) * B ( * ' ( U HI; * HI2< 34 R=; E 6 6* E (< ( E B* * E " 6 ' ' < 9 ' * * B* 6 < H '* ( '* E ) * & B* 6 B* 6" & ( # ) % ) ' - 0- 9 ' 4 % 6 E * * * * & ) ( 6 % % ' *6 @ B * 0 * ' %- E ,* % * " < A '6 H * ;E % 3. .. (L 8 19: ,;9< + ? @ * ;< " '3 @ B' ( - µ , µ< 6 B' % )0 12 3 + : 9% 6 % % # * ( & % − 6N 6 D ( ( %- 3 * * " " 9% < αM< 6 6 C ,* ' W ( * 6 * C ( ' H I α; E % % α3E # ;N H + > & ) − * @ ( 9< B* * " B 0, # - 0- / ( 4 B* * * Hµ - µ % @ A µ !* 6 ) * & % B' # & ) µ D BC " % B' # 9< + % % # % # 5 ) 24 62 5 ? * 6 * / ) * % % # & ) " 7 - @ ( B*... > J ' & F ,* & % B 90.0% CI 70. 13, 75. 43) ( *& 6 * B* 6 ( H7 37 2; %- % B' # % Histogram of Age (with 90% t-confidence interval for the mean) 7 6 Frequency 5 4 3 2 1 _ X 0 [ -1 55 60 65 70 ] 75 80 85 90 95 Age W* " $ %& ,* " * 7 * R2 () , - , "/ (( H ?, > % I , > > +$D + ,* % ) 0' ' ) , , & * " ! 9< @ & A * 6 , (< B* ,* X # 3 * N % 6 π 6 H I π; 2 / 36 '( * 6 * 36 6 0 1 M B BC & & ) * 6 & 6" (% . 3 2 0.061812 0.08 837 6 4 3 0.1 133 23 0.201699 5 4 0.155819 0 .35 7518 6 5 0.171401 0.528919 7 6 0.157117 0.686 036 8 7 0.1 234 49 0.809485 9 8 0.084871 0.89 435 7 10 9 0.051866 0.9462 23. ' <"#=6 899%#1$ 0%>!+ ,- '*> -7 0K) ,- ,0 - ( C;&$ -7 0),P(I) ,- %,0 - &(16 D""#.,0 - (6 CIN L&$*,)( -7 0D%2' . AA 899%:1$ 0%>!+ ,- '*> -7 0K) ,- ,0 - ( C;&$ -7 0),P(I) ,- %,0 - &(16 D""#. ,0 - (6 CIN )L&$ *,)( -7 0 D% 2 ' 899%+1$ 0%>!+ ,- '*> -7 0K),-