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We have a sample of data and a statistic (e.g., the sample mean). &f   ̙337 / ___PPT10 .0+h[ D/' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(++0+5 ++0+5 ++0+5 +"l 0 (   T  H?Rectangle 1"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!*drs/downrev.xmlDN1E&CLH H!5I>uVƅ.o͹9Eo[q&c qZD[ǤJۛ]xK2"A8䨠˥ UCuĩ;8o1k=^ܶrecipzhUCթ >6OݪԼ2R~"Ra-W `ⰾ[ L%PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!*drs/downrev.xmlPK I,$5 HTraditional method: Use theory to study how the statistic should behave.2I Hf.fI  S  H8?Rectangle 1"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!p drs/downrev.xmlDAN0EH$6: T ԭP5zi:ᮓ1o`ڳ?ڗ.v"Ӑy7<|8mkLvcS9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!p drs/downrev.xmlPK ,$5 GBootstrap method: Use a computer to simulate how the statistic behaves.2H Gf.fH    H?Rectangle 1"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Vdrs/downrev.xmlDAO1F&fLbJ!AW⅕xöm7mxMޗ7wa'A;+`8ȀԶZ'BD+q\(|v{3\Щ5KrblsC`lb{ tK$7 Ȳ17mZPBQu(Fz. sxүcx)D{y+௪el~y-7"y).&|vPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Vdrs/downrev.xmlPK  0,$5 ,Brad Efron, 1980s   infinitely intelligent, but he doesn t know any distribution theory 2Z Yf.fZ   ̙337 / ___PPT10 ._Ҽ+h[ D/' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* %(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* %(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* %(++0+ 5 ++0+ 5 ++0+ 5 +"t ogP(O(  (# (  x!0e0e?Rectangle 2P  5 W The Bootstrap f   ( L8"?Text Box 4  pzWe wonder what would happen (how would a statistic behave) in repeated samples from the population. Basic idea: Simulate the sampling distribution of any statistic (like a sample mean or proportion) by repeatedly sampling from the data. A  pseudo-sample is to the sample as the sample is to the population. 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-0.50504 -0.08999 *3>*B ppt_xB ppt_y=@BB3F>0<* @D' = @B%(D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy' =.A7 BBBBBSM -0.40382 -0.52741 L -0.40382 -0.13879 *3>*B ppt_xB ppt_y=@BB3F>0<* @D#h' = @B%(D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy'  =.A7 BBBBBSM -0.55503 -0.50081 L -0.55503 -0.11219 *3>*B ppt_xB ppt_y=@BB3F>0<* @D' = @B%( DL' =AB*BB@B0B%()?)?))?Ds' =.;7 BBBBBMM -0.4967 -0.52302 L -0.4967 -0.1344 *3>*B ppt_xB ppt_y=@BB3F>0<* @D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy' X=.A7 BBBBBSM -0.53837 -0.54523 L -0.53837 -0.15661 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(4DR' =AB*BB@B0B%()?)?))?Dy' =.A7 BBBBBSM -0.38836 -0.56743 L -0.38836 -0.17881 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(( DN' =AB*BB@B0B%()?)?))?Du' =.=7 BBBBBOM -0.5967 -0.58964 L -0.5967 -0.20102 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%( D2' =AB*BB@B0B%()?)?Dy' =.A7 BBBBBSM -0.48004 -0.61185 L -0.48004 -0.22323 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(D.' =AB*BB@B0B%()?)?Du' =.=7 BBBBBOM -0.5967 -0.65625 L -0.5967 -0.26764 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(D2' =AB*BB@B0B%()?)?Dy' =.A7 BBBBBSM -0.55503 -0.68957 L -0.55503 -0.30095 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy' =.A7 BBBBBSM -0.55504 -0.70067 L -0.55504 -0.31206 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy' =.A7 BBBBBSM -0.61336 -0.72287 L -0.61336 -0.33426 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(DN' =AB*BB@B0B%()?)?))?Du' =.=7 BBBBBOM -0.5467 -0.73398 L -0.5467 -0.34536 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy' =.A7 BBBBBSM -0.63004 -0.76729 L -0.63004 -0.37868 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(8DP' =AB*BB@B0B%()?)?))?Dw' =.?7 BBBBBQM -0.54948 -0.4254 L -0.54948 -0.03678 *3>*B ppt_xB ppt_y=@BB3F>0<*@D' = @B%(DR' =AB*BB@B0B%()?)?))?Dy' =.A7 BBBBBSM -0.78836 -0.76729 L -0.83836 -0.38977 *3>*B ppt_xB ppt_y=@B̼BMJA>0<*@D' = @B%(XDL' =AB*BB@B0B%()?)?))?Ds' =.;7 BBBBBMM -0.5467 -0.8117 L -0.4967 -0.40088 *3>*B ppt_xB ppt_y=@B<BWR>0<*@D' = @B%(DL' =AB*BB@B0B%()?)?))?Ds' =.;7 BBBBBMM -0.6467 -0.83391 L -0.6467 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=AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.50781 -0.60305 L -0.50781 -0.21443 *3>*B ppt_xB ppt_y=@BB3F>0<*"DD' = @B%(xD2' =AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.69115 -0.58085 L -0.69115 -0.19223 *3>*B ppt_xB ppt_y=@BB3F>0<*#DD' = @B%(D2' =AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.64948 -0.62526 L -0.64948 -0.23665 *3>*B ppt_xB ppt_y=@BB3F>0<*$DD' = @B%(@D2' =AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.58281 -0.68077 L -0.58281 -0.29216 *3>*B ppt_xB ppt_y=@BB3F>0<*%DD' = @B%(D2' =AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.61615 -0.70298 L -0.61615 -0.31437 *3>*B ppt_xB ppt_y=@BB3F>0<*&DD' = @B%( D2' =AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.64948 -0.72519 L -0.64948 -0.33658 *3>*B ppt_xB ppt_y=@BB3F>0<*'DD' = @B%(l D0' =AB*BB@B0B%()?)?Dw' d=.?7 BBBBBQM -0.79982 -0.71458 L -0.90816 -0.3037 *3>*B ppt_xB ppt_y=@B]]Bh?R>0<*(DD' = @B%( D2' =AB*BB@B0B%()?)?Dy' d=.A7 BBBBBSM -0.55781 -0.79181 L -0.46615 -0.32547 *3>*B ppt_xB ppt_y=@B=;=Bn>0<*)DD' = @B%(4!D0' =AB*BB@B0B%()?)?Dw' d=.?7 BBBBBQM -0.80782 -0.7585 L -0.90782 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=-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD ' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<* X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* XD' =-o6B fade*D3><* XD ' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<* X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* XD' =-o6B fade*D3><* XD ' = @B%(D ' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<* X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* XD' =-o6B fade*D3><* XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD ' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD ' = @B%(D^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD3' = @B%(D' = @B%(DQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XDQ' =4B5BB@B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*XD^' =AB5BB@B0B%(D' =1:Bvisible*o3>+#.<*X%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*XD' =-o6B fade*D3><*X+0+0+X5 ++0+X5 ++0+X5 ++0+ X5 ++0+ X5 ++0+ X5 ++0+X5 ++0+X5 ++0+X5 ++0+X5 +"+  0`(  `/ `  x0e0e?Rectangle 2P  5 cA small bootstrap example f  G ` F?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDn0ET8KM ԇ`CXC#u!m'YZl]z0ӫm0u>U6nm0YR7zi8_V+x(y3Bl)PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK P`@,$5 RConsider these 7 data points on the variable Y = pulse: 48, 50, 60, 66, 68, 72, 90S S$fS    ` F?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!hRedrs/downrev.xmlDMO0 @HH\KBݲi|IM5&g=-D!v) ;*_ADFLa:?[b*:Yb PJC2;`ZYn{ySwb=jV̧!FS4X+uy6 L[U[[ru02yS3PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!hRedrs/downrev.xmlPKPp,$5 /The (sample) mean is 64.9 (and the SD is 14.3).0 0$f0  u ` FP?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!$Kdrs/downrev.xmlD1O0Fwب"VCt?kۑ}4 ;Ool/b睂| xݹVAv"2:w`f;ĭH T`B~ JpLrˇ,{; b<}Y̺yvɚJN3ϕ.?:Ԓ#F ťԄ@n~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!$Kdrs/downrev.xmlPKI ,$5 Let s take a bootstrap sample, by writing the 7 values on 7 cards, shuffling, and making 7 draws with replacement. Then calculate the mean of those 7 values. (We can call this a bootstrap mean.) $f    ` F?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Z6drs/downrev.xmlD1O0Fw$uبJ VU)Kt?k%#hާ$ۋz`1/@n]:?Nc)(f}RvFd%*0C)e Ys?Egh8f( *`Tm<\h +fi )ҹ_A%Z}东PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Z6drs/downrev.xmlPK` ,$5 |Repeat this a few times. $f  E ` F?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Gdrs/downrev.xmlDN0HHܨSUOKK8"^G$oŁWOXSG l`>+@_A%A&%X-X0{iTp*рKSc8C%6Eq=x"v=g+c./(QN6܀:N_;LB@˩^PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Gdrs/downrev.xmlPK@`,$5 TThis is tedious. Technology helps& StatKey& + +$f+   ̙33me___PPT10E..+_6D ' = @B D ' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*`%(D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*`%(D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*`%(D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*`%(D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*`%(++0+`5 ++0+`5 ++0+`5 ++0+`5 ++0+`5 +"  KCPh+(  h0 h  x0e0e?Rectangle 2P  5 dBootstrapping with StatKey f  4 h F?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!eU&drs/downrev.xmlDN0DHH\uPzhK/6^zhFoD!6)'r׍oO "zG F\\^̱оw{: b sWH+CwRw"j n[yeb҃^ U߇Y\۸ɪ,V Ow<6Zl6Aǯ=F %d r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!eU&drs/downrev.xmlPK p,$5 We can go to StatKey, choose Bootstrap Confidence Interval and choose CI for Single Mean, Median, Std. Dev., choose any of the built-in data sets and click the Edit Data button, and then type in our data (48, 50, 60, 66, 68, 72, 90). p $f$ $f%$5$f $A$f  T h Hp?Rectangle 1"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!'Qdrs/downrev.xmlDN1E&CHi%2PA#aLeN 3OB7ܜ3 ;Y w#l锶*l% =X.Ws̔;-X!C umy(k2F%c9MBLAmC-j*ŏ_V9>NMXJy=g"u?EJ{"y -&K PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!'Qdrs/downrev.xmlPK `  ,$5 AThen the Generate 1 Sample button will create a bootstrap sample.8B $f$'$fB  # h H?Rectangle 8"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Ζdrs/downrev.xmlDQO0M5@1( 1a nl] ';ft>hgS6Ddu2…,W3ʕ;-؈!'6>2- c׳MyC1EHওY6M-l>ay업:N]Tf# / "L}ZB!LAVk#$d,APK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Ζdrs/downrev.xmlPK  0,$5 -And we can get 1000 bootstrap samples easily.. .$f.   ̙337 / ___PPT10 ._`+D/' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*h%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*h%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*h%(++0+h5 ++0+h5 ++0+h5 +"C  ,,p p+(  p0 p  xЬ0e0e?Rectangle 2P  5 dBootstrapping with StatKey f   p F0?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Hidrs/downrev.xmlDN0EH5H uMK4X^L' ^CP 7tP\݃H`I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN1E&CHh̨#8c$a>´q˛{snt>؎(D㝀I\qJ XL$vޑ EFWS?5XXR_q[Mrb1(.3v(JnѸ|[fYټԏMwa,ѐ[U+QP\v5DA@v˦PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK p,$5 We can make a 95% CI for via $f    p H?Rectangle 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!cdrs/downrev.xmlDN0DHH\݀P nDRC616i8q47z`ZѳY 7 )mk Ϸ{!U:`>;?R/c-Ć$41v9b6FcbF,!mCC/发[n~U1)3܎_ADkEJZ)D[2MPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!cdrs/downrev.xmlPK 0 j,$5 uEstimate 2 * SE $f   p HP?Rectangle 7"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!]drs/downrev.xmlDAN0EH$6: JBD j41vX,`9-FӋ#Ed 6Ni"lo B$w`1QɮXV$ !t1PmvTN nzye4mjhe;>UPm?כ6C_AD_*B8oVk =BrKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!]drs/downrev.xmlPK A`P ,$5 p 64.9 2*(5)  $f    p Hp?Rectangle 9"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![drs/downrev.xmlDN0 @HCd$.KAh@Y6쀴5^$U8~ֳl1^(D㝂I\qzzu"&t{H",g3,?5 X.26Y?cb1R<&ϧҢqÁ5*x_ݮe)9+\n/J]^O 86U[8evTF ?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-![drs/downrev.xmlPK ` ,$5 m 64.9 10  $f    p J?Rectangle 10"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!բdrs/downrev.xmlDN1&C3&^RAXxa;VVXƃ'iٙ|J0SvW`!U:K`1an\ƚ% Jhb2CՐ0p5W/InZ"Ę6-4ѪX bTV9>NS>)ߏ?||o",Nn$Uj;|]^ H^BK PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!բdrs/downrev.xmlPK j ,$5 p (54.9, 74.9)  $     p N?Rectangle 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!4drs/downrev.xmlDN0EH5HlPGBUT,~O؎l_,Gwt=`ZѳqmTckj4"YEpŜr厶~k 6䄠cr)CPm* tZ*O7Ͳ4Ԡacnt}WJMK}z4jx~y Qkp0O㫷7#$dLA.PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!4drs/downrev.xmlPK0 ` ,$5 "Good news: We can bootstrap a difference in means or a regression coefficient or& R R$*P       p T0?Rectangle 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!u{udrs/downrev.xmlDQO0M5@+"I!1`Hx]/ζm|Ǔs|Ek֒5̪ 0(! nf({6{jӐ1>A EM¹ !uC.9u͇BćZU鏖paӥXթ^Hyw۽< ԅxN7U&)JGI~6PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!u{udrs/downrev.xmlPK `0,$@ 5 Bad news: Bootstrapping when n is small does not overcome the problem that a small sample might not mimic the shape and spread of the population. : -$$c$   ̙33___PPT10._`+D' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*p%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*p%(DW' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*p%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*p%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*p%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*p%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* p%(D' = @B%(D' = @B%(D' =4@BBBB%(D' =1:Bvisible*o3>+#.<* p%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* p%(++0+p5 ++0+p5 ++0+p5 ++0+p5 ++0+p5 ++0+p5 ++0+ p5 ++0+ p5 +"(  x(  x x H?Rectangle 8"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN0DHH\u@mU7ilGiӿьMđ}"܍2l+m'!U9g0]^L)Wd|,c#Ć\Pl(\6ub)M'l, iZyru( a]0/7cjX<I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!7kIdrs/downrev.xmlDQO0M%HB b{cz*kƿAOw-V؉Wx'V*v3`>YC.aY`&lTE hC3}ݒF?=bt ;$)רL|huK>IQs}|QoL>q7^ \_MWr)` q;%9-FK+PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!7kIdrs/downrev.xmlPK `,$5 8And what if we want something other than 95% confidence?9 9$f9   x H?Rectangle 7"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDAN0EH$6:E(@贪 `O؎lӤbl1N,t`[;m|}"YEpŌ S 6ReCaz);8o(7Ryt.riHRϫcm7ݪ_'rS>T篈WD1?z QBHk#$d,APK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK ` ,$5 nWe can take the middle 95% of the bootstrap distribution as our interval. Or the middle 90% for a 90% CI, etc.8o $f $T$fo   ̙33___PPT10._ +oaD' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*x%(DY' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*x%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*x%(++0+x5 ++0+x5 ++0+x5 +"@  ** *(  +   x0e0e?Rectangle 2P  5 _Recall the pulse data f  !  Fp?Text Box 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!:7drs/downrev.xmlDN0EH5H^"iݪ8jl{hb˫{ub5N(;,AuDdt;HDVnK7"A\,QaK)cmb\>XC#u!m'^Zl]z0ӣ :g7`+./*^/jm6Cl)PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!:7drs/downrev.xmlPK p,$5 ,n=7, data are (48, 50, 60, 66, 68, 72, 90). - -$f-    H?Rectangle 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Mdrs/downrev.xmlDN0DHH\u@(PBD[Combm8q47zh{q c7 qVz "DdcRp 펼C[  T8R#a휷S n{yeh8=t8вf_[,K0W}m"/QV/ r+Hn4YPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Mdrs/downrev.xmlPK ,$5 We can made a 95% CI for via $f     H0?Rectangle 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!cdrs/downrev.xmlDN0DHH\݀P nDRC616i8q47z`ZѳY 7 )mk Ϸ{!U:`>;?R/c-Ć$41v9b6FcbF,!mCC/发[n~U1)3܎_ADkEJZ)D[2MPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!cdrs/downrev.xmlPK  ,$5 uEstimate 2 * SE $f    HP?Rectangle 7"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!]drs/downrev.xmlDAN0EH$6: JBD j41vX,`9-FӋ#Ed 6Ni"lo B$w`1QɮXV$ !t1PmvTN nzye4mjhe;>UPm?כ6C_AD_*B8oVk =BrKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!]drs/downrev.xmlPK 0 0,$5 p 64.9 2*(5)  $f     H0?Rectangle 9"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![drs/downrev.xmlDN0 @HCd$.KAh@Y6쀴5^$U8~ֳl1^(D㝂I\qzzu"&t{H",g3,?5 X.26Y?cb1R<&ϧҢqÁ5*x_ݮe)9+\n/J]^O 86U[8evTF ?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-![drs/downrev.xmlPK p` ,$5 m 64.9 10  $f     J?Rectangle 10"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!բdrs/downrev.xmlDN1&C3&^RAXxa;VVXƃ'iٙ|J0SvW`!U:K`1an\ƚ% Jhb2CՐ0p5W/InZ"Ę6-4ѪX bTV9>NS>)ߏ?||o",Nn$Uj;|]^ H^BK PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!բdrs/downrev.xmlPK p  ,$5 p (54.9, 74.9)  $     J?Rectangle 11"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!̢drs/downrev.xmlDAN0EH$6uPPBDR`OxlӦb7[ G8Vp;@Nnl7o!"k3X//fkw5؈$ᐣ6>2-Y c'wbLoxJrIMEiŞ-Շ*XwvYãy)LJ]_ O " >\U_USF1D R\JMPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!̢drs/downrev.xmlPK  W ,$5 Click the  Two-Tail button. The middle 95% of the bootstrap distn is:F A$f,f$fF    JЗ?Rectangle 12"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN0HH\uQSB !'xvd6}{Vบ|r8P;7 kZi#'\ͱtS+Xb Btd1N@Jr,JB:jU^WU)Ln/J]^O ,Rsi^cLp2PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK  P ,$ 5 p (55.4, 75.1)  $    ̙33___PPT10._0$+JD' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =ABBB@B0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(DW' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(DY' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* %(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<* %(++0+5 ++0+5 ++0+5 ++0+5 ++0+5 ++0+5 ++0+ 5 ++0+ 5 +"+ (  A   x00e0e?Rectangle 2P  5 u+Bootstrapping other statistics: Correlation,, f,    J?Rectangle 11"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!:ƒdrs/downrev.xmlDN1&C3&\R>v+vXƃ'ؙB4Ix `jk$T_/bB$\)b~{3BѹL  ЦǺ%q{r|^v|"Ĕ[4./ӲXi[->սz.OR7`,P-`>Ø(Hq95#PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!:ƒdrs/downrev.xmlPK  7 ,$5 ,Click the  Two-Tail button. The middle 95% of the bootstrap distn of correlations is:V A$f,f$fV    JhO?Rectangle 12"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Ydrs/downrev.xmlDAO1F&fLtD+X9xne;ݴoA7y_tVX0A\9mVx܁Yc(|v~6\#PZ$ 41vjb8c:}-cVdXZ4hP/hYkoIYˋ~"RG ZnA^O[oC$ ťԄ@~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Ydrs/downrev.xmlPK 0  ,$5 p (0.72, 0.87)  $     JO?Rectangle 13"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!pdrs/downrev.xmlDAN0EH$6uJ)n Pi416mr{F,`9z޶D!܎3*>_Gs1zG Z^^,0t*S-Xb \X5d1}GPKrIͤEx U*xL7u!/3(u}?=HԧIu7WUhn8 `c8PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!pdrs/downrev.xmlPK `,$5 !We can bootstrap a correlation. Consider the Commute Atlanta (Time as a function of Distance) data. The sample correlation is r=0.81.T -$f1$ $f$$f  N  J?Rectangle 10"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Qէdrs/downrev.xmlDAO1F&fLh1q+J<am7mxMޗ7wa'A;+a8ȖNi[I~'BDq$\(|v{3LЩK2Pf&aZ7+<4A17mZEM8 zI/Bx%e{yς_?*Wel~y6"y ).&|vPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Qէdrs/downrev.xmlPK   7 ,$5 VGenerate 5000 bootstrap samples. Each time, get the correlation b/w Distance and Time.W W$fW  !  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If we don t trust a t-test or t-based CI, how might we bootstrap? $f  :   x#"0e0e?Rectangle 2`$  5 n$Bootstrap and Regression/Correlation%%$f%    HX'"?Rectangle 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!͸nrdrs/downrev.xmlDN0DHH\PnZPCo mMLc;MX8|08Y w )m ۏG!U9`>RnXF$ Ihc Pl(\6u{ })M,ѐ顥-ׇHx_߯?OzyS>TW)g?帟|RIAWjC!ܒiPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!͸nrdrs/downrev.xmlPK @`0,$5 (1) Randomly resample (x,y) pairs and fit a regression model to the new  boot-sample. W W$fW    Jx7"?Rectangle 12"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN0xk+q͏ u+T@r@ }mMLc;M}-p\j>b՛FrJZXhΒfʝlA2,IlPBcq &w`LxJr!fܠi UHxm$/^Os`\[`a*0DR\JM PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK  `,$5 .If we think of the x s as fixed (e.g., a designed experiment), then (2) looks good. If not, then (1).f f$ff  y PS81xvQ C (Group 3#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1drs/downrev.xmlD[k@ }hEW)x=&ِ&w >3 \w ծ D S \5IW%&ڶ|3 T{_%R4'n`+mmYgR)0&`a!NJ9ӷQbŻozI~Y_S+OGs\PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1drs/downrev.xmlPK`# ,$D5<  J6"?Rectangle 10PS81xvQ 8(2) Randomly resample the residuals from the fitted model and attach them to the (fixed) (x,y) pairs. Then fit a regression model to this new  boot-sample. : $f $fz$f    J1"?TextBox 2L|s7=yl@ e^ $f   ̙33  ___PPT10e .]aRx+xnD ' = @B D@ ' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(DN' = @B%(D' = @B%(D' =4@BBBB%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(++0+5 ++0+5 ++0+5 +"%# (    H2"?Rectangle 8"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!&drs/downrev.xmlDN0DHH\u@mZ徉ilGۦ|=8fFo:L'vn`[;mݼ>YF8sbJr'c 6ReCaz9o(<t>Ґ顥-`>V_^e&+ "fy+QBؽ+՚Bdܒi9PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!&drs/downrev.xmlPK P,$5 How does one actually do this? $f  0   x3"0e0e?Rectangle 2`$  5 dImplementing the bootstrap$f  %  Hx."?Rectangle 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!%oQdrs/downrev.xmlDN0DHH\u@PBD j6$&K=8fFom/N$AڸFDdt{H",gs̵?-JnDyȥUKRW`S  n{yeSiѸ@ ֛nUȯ<_2R#\_*Fo12-&KPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!%oQdrs/downrev.xmlPK 0 ,$5 .If it is 1991, then maybe write your own code./ /$f/  m  H4"?Rectangle 7"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Hdrs/downrev.xmlDAN0EH$6: T ԭPk416uz{F,`9[&;#hSp3+@k6U|~:wDVgcZKTХ4RƦ#qGr| 3 ob.- ocs٭+?.~"є_TibL%PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Hdrs/downrev.xmlPK  ,$5 xToday, use software such as StatKey for a small problem in a standard setting (1 mean, 2 means, simple regression, etc.)y y$fy    Hx4"?Rectangle 9"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!vXdrs/downrev.xmlDN0 @HCd$.Th@Y6׆5I{,p7[G xn xm\`}}:wLˋڟ܆UjK\,PAPH,Ɖ1`1ZXn{gTZ4?t8вP}[z,ɼޔU&RW3Dc?s_US:(( 29PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!vXdrs/downrev.xmlPK  ,$5 In general, use R and either (a) write a function for the statistic you want to bootstrap and use the boot() command or (b) use the do()* command in the mosaic package. $f   ̙33  ___PPT10 .^apm+[D ' = @B DM ' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(++0+5 ++0+5 ++0+5 ++0+5 +" (  k  H7"?Rectangle 8"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!b3drs/downrev.xmlDN0DHH\uPBx6mX8b8ƱQvp`}"1)8Sbv'ұH9*hcs)Cݒ0r=q[)FjgDZ4ZiR}(f,aj^o2d "+QV0;W-H^ArKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!b3drs/downrev.xmlPK P,$5 sA consulting client recently needed a CI for a ratio estimator, so I wrote a short script in R. Here is part of it:t t&ft     x1"0e0e?Rectangle 2`$  5 QExample$f     NX-"?Rectangle 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!}Fdrs/downrev.xmlDKK@aNl1i)/MA]3I0s'̌i\7[9_[Vp1J@V\*)56I<,'3̴M(EPABI鋊 mc`ѕR;Gi8IRiPaK7ߛm0_?> T~y "P|C=hd<?|Zr _ PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!}Fdrs/downrev.xmlPKA,$D5 j4ratioBoot <- function(mydata, indices) { d <- mydata[indices,] # allows boot to select sample ratio <- sum(d$Y)/sum(d$X) return(ratio) } mydata=ratio.data #this is the client s data file library(boot) #make the boot package active bootratios5000 = boot(mydata, ratioBoot, R=5000) boot.ci(bootratios5000, type="norm") #gives 0.1236 to 0.2486 boot.ci(bootratios5000, type="perc") #gives 0.1221 to 0.2479 hist(bootratios5000$t) #a histogram of the 5000 values mean(bootratios5000$t) #gives 0.1847 sd(bootratios5000$t) #gives 0.0316 A"&C" &"&W"&%"&" &"&"&   ̙33___PPT10t.aُ+ :D' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(+p+0+5 ++0+5 +"W S K 3 (  J  H4"?Rectangle 8"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!1%drs/downrev.xmlDN1E&CLh H!51L_'mm\ޜ3' zV0*@7^[nl7/ bBy&0]_Mk:թ±D&26Ƒsa1R:jab纐R7+DCk6EUZ V1& [6͖ g?PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!1%drs/downrev.xmlPK P,$5 SThe mosaic package in R has a command that will do something (anything) many times.T T&fT  -   xX3"0e0e?Rectangle 2`$  5 aUsing the do()* command$f  t  N5"?Rectangle 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!S.jdrs/downrev.xmlDKK1!\Mi38-cRjkr;$Cop9|o:LZA;+f#+Ҷ='BDv)|vy1BP%K PY0p 7S%WO nj>̲6=T}Ekmz׽Ǘ2o+\WX.c)`$dL~PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!S.jdrs/downrev.xmlPK,$D5 dlibrary(mosaic) pulse=c(48, 50, 60, 66, 68, 72, 90) mean(pulse) mean(resample(pulse)) do(5)*resample(pulse) do(5)*mean(resample(pulse)) mymeans = do(5)*mean(resample(pulse)) mymeans mymeans = do(10000)*mean(resample(pulse)) hist(mymeans$mean, breaks=100) mean(mymeans$mean) sd(mymeans$mean) quantile(mymeans$mean, probs=c(0.025,0.975)) #gives 55.7 to 75.1*e Q"&e   ̙33___PPT10t.d+ :D' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(+p+0+5 ++0+5 +"> (    H,"?Rectangle 8"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!FNdrs/downrev.xmlDN1E&CLh1eV21}0 ]ܛss&4L>hg% )m+ GXh6Β+M&)w:b bCیPd0]K6u }ŕK? 1M5<?Fj=\9?))ߏR>>t7`?WWP0vV L%/PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!FNdrs/downrev.xmlPK P`,$5 #There are yet other variations on the theme. E.g., the "wild bootstrap" in which you keep each residual with its observation, but randomly multiply the residual by -1 with probability 1/2.  &f  2   x8/"0e0e?Rectangle 2`$  5 fThere is more& $f    J/"?Rectangle 10"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!UQ1drs/downrev.xmlDJ0!҉NˆL:Y5m\sRu> <|-ۉ=`+3ĕӆ[!"k#XOOfkw5؈$ᐣ6>2T-Y c'V;o17R{<$eMEiŞ-U*x]]6B~㨸)3>)u~6<܃4QUN-q^cPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!UQ1drs/downrev.xmlPK `8 ,$5 [Bootstrap tilting: Reweight the data to satisfy a null hypothesis, sample from the weighted distribution, then invert a hyp test to get a CI.] &f    H/"?Rectangle 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!n drs/downrev.xmlDN0DHH\AP ԭPʩx٦M8fFo2\'f@Xn4߯AĄlLa6=?`aR#2cڔBX0|OS&!]'oKC=[wՏ[UP)i}y1+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(++0+5 ++0+5 ++0+5 +"m 0(  .   x:"0e0e?Rectangle 2`$  5 b References& $$f      Hx:"?Rectangle 6"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Z drs/downrev.xmlDN0DHH\u@PBDRC?`o؎m=8fFom/N$AڸVDdt{H",s̵? +nEyȥMGR"Z>˦ҢqÁV5`ˇr*ɼ*M)W `bqLAArKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Z drs/downrev.xmlPK `g,$5 zTim Hesterberg s 2015 paper  What Teachers Should Know About the Bootstrap: Resampling in the Undergraduate Statistics Curriculum in The American Statistician. See http://amstat.tandfonline.com/doi/full/10.1080/00031305.2015.1089789` &fg&&f&fK&f  p  HX<"?Rectangle 5"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Gxkdrs/downrev.xmlDQO0M5H!C&8x\ZYۥ0xrNoLvVx#8m+`|~"Z$J9]lE:,Al(P/8"az;:o0[.=^t%rnPTd_4O!aX4x2UJ9൬0D[2MPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Gxkdrs/downrev.xmlPK @  ,$5 GEfron and Tibshirani (1993) An Introduction to the Bootstrap, Springer.PH &f && &fH    H8;"?Rectangle 1"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Kdrs/downrev.xmlDN0DHH\*jSn[C{4#۴)__ggFoLvVX#[;m#av,D ;gI‰,3̕;ذ!G m}y[2Ʈ'c1M'BdܠiŞ}m$|,uQ~U X!?mFEJB&d{?mV+ tI PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Kdrs/downrev.xmlPK9 ,$5 mThis is a summary of a longer (2014) paper with the same title, available at http://arxiv.org/abs/1411.5279. n n&f*M       Mk ̙337 / ___PPT10 .a!+XD/' = @B D' = @BA?%,( < +O%,( < +D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(D[' = @B%(D' = @B%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+#.<*%(++0+5 ++0+5 ++0+5 +"a;- (      0e0e?4Slide Image Placeholder 1   5H   (T0e0e5%?(Notes Placeholder 2 0  5 6     lQ?6Slide Number Placeholder 3_   l*(2      V`?&Date Placeholder 1    p*(2  [     `^?*Footer Placeholder 2_P   V 2"     I}OPM80___PPT10.bX a=-  (      0e0e?4Slide Image Placeholder 1   5H   X0e0e5%?(Notes Placeholder 2 0  5 6     l?6Slide Number Placeholder 3_   l*(2      Vx?&Date Placeholder 1    p*(2  [     `?*Footer Placeholder 2_P   V 2"     I}OPM80___PPT10.b` V- nf@$N(  $  $  0e0e?4Slide Image Placeholder 1   5 $  0e0e5%?(Notes Placeholder 2 0  5 The quote is from David Freedman, who was exaggerating. 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(c) is fairly common but often doesn t work well. (d) and (e) are better but are harder to do. T method: (theta-hat  q(0.975)*SE, theta-hat  q(0.025)*SE), so (a) we get quantiles from bootstrap t-distribution rather than from a t-table; and (b) we subtract an upper quantile of the bootstrap t-distribution to get the lower endpoint.     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V."?&Date Placeholder 1    p*(2  [     `85"?*Footer Placeholder 2_P   V 2"     I}OPM80___PPT10. q- t(     0e0e?Rectangle 2   58   8,"0e0e5%?Rectangle 3 0  5 6     V,"?&Date Placeholder 1    p*(2  [     `X0"?*Footer Placeholder 2_P   V 2"     I}OPM80___PPT10. l-  t(     0e0e?Rectangle 2   58   5"0e0e5%?Rectangle 3 0  5 6     VX6"?&Date Placeholder 1    p*(2  [     `7"?*Footer Placeholder 2_P   V 2"     I}OPM80___PPT10. n- @t(     0e0e?Rectangle 2   58   0"0e0e5%?Rectangle 3 0  5 6     VX9"?&Date Placeholder 1    p*(2  [     `;"?*Footer Placeholder 2_P   V 2"     I}OPM80___PPT10. r}G{{W ~#ߋܶk] G c A E Q0 HF m 0 4 N   2 N  # ) 2. 3 8 = B H M :R VW r\ d i o t y  3 O : Oh+'0$ `h   STAT 113 for 9/11/15 jawitmerPatricia Armstrong79 Microsoft Macintosh PowerPoint@X@P9d@O@0§'e ՜.+,D՜.+,0     On-screen Show (4:3)| "Times New RomanMS PゴシックArialCalibri WingdingsDefault DesignNotes on BootstrappingPowerPoint PresentationPowerPoint PresentationThe BootstrapThe BootstrapPowerPoint PresentationSampling DistributionBootstrap DistributionPowerPoint PresentationThe BootstrapThe Bootstrap ProcessA small bootstrap exampleBootstrapping with StatKeyBootstrapping with StatKeyBootstrap Percentile CIsRecall the pulse data,Bootstrapping other statistics: Correlation)Atlanta commute correlation bootstrappedBootstrapping other statisticsPowerPoint PresentationOther Bootstrap CIs%N.B. We use the bootstrap to get CIs%Bootstrap and Regression/CorrelationImplementing the bootstrapExampleUsing the do()* commandThere is more… References  Fonts UsedTheme Slide Titles4 8@ _PID_HLINKSA http://arxiv.org/abs/1411.5279http://arxiv.org/abs/1411.5279*_C Patricia ArmstrongPatricia Armstrong  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./023456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~     !Root EntrydO)Pictures`Current UserSummaryInformation(PowerPoint Document(1g DocumentSummaryInformation8