中央極限定理 (Casella and Berger, 1990)
從平均數為
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEiWCwrky6Af4np3YV9w6ic7yHV4oL1VB0uXklXtod994lBL84egDewJTgL0Kn-giYZV3vJ0jQEiU3mkuvpvelJJPIiNGwiUBYDP-ObsavMq1644alkD4SpSwpSCz3i0oGAIx1PL4LI2wRcV-MIMbNee_CqeXg78kpsftb6OeaYr0a_tdMuU=)
,標準差為
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEjvdtVWzubCLo7pQuiO8Vj1oVm-vll7lzJYfZCFfhwAyiQlpoptlZKmSAnfhS6tdCwn2bNGyyzY3876kOnCdSLZSNH2Og4dWaoPa5OkRJZ_p5WO6BvUw5vUhhLszF9mUE2-nMhV2ESWuIi8FTe8h2dvtydm-XktAVWV1r-gh1hdewmfQ02E=)
的母體中(不論母體是何種機率分佈),隨機地抽取大小為
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhU_Voo5qcmuZQltrWO4Kb83o4Nx01KJb59lG4clNsUsi2T9MQDaSbg60U01qTF8EDJgtS2viQopJ9Dk2EeGrf-U17Nwr5djFHUld9gWZKM0WrSB3ojiWLCx_ryT40oPKFAId8AxNhYpi7s8Sb05SzE3P5WLbWRPp5UaRJp67wABfr6Vy2Z=)
的獨立樣本
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhK3_8JvyptXzrL8RFKj4vnusTz1e3fKosUz67Ama-ejPXEJ4L-Fhzui2Lbgos8rdVxuWKc-lh-aUeFCoaU3TQx1u7qZgYVlthKBgzOPz95LZez8JXhJ36P4wRwjP38JQxEBjf3aWUXwslrLUyX2XprHF3RSgH78mpSkTdTn3bPeOBh_EOi=)
。只要當樣本數
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhU_Voo5qcmuZQltrWO4Kb83o4Nx01KJb59lG4clNsUsi2T9MQDaSbg60U01qTF8EDJgtS2viQopJ9Dk2EeGrf-U17Nwr5djFHUld9gWZKM0WrSB3ojiWLCx_ryT40oPKFAId8AxNhYpi7s8Sb05SzE3P5WLbWRPp5UaRJp67wABfr6Vy2Z=)
很大時,其樣本平均數
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhX45X8OsYNoQJ0KVFkyhYsybNojpJ72rSl2mDUJ630wCHrY19KJYRBWeHoz9N5hD1XSWkllGqOrGiMvyXLaw4DCVzo9ptYjW1jByKSS21g0YMZpiIlpx2FSUgcvs_1F-MoUeTdzX6pJur9evb62fQMHaKZb5Z3IseO4vIb_Ta7vVuMU-8c=)
會是一個常態分佈。
因此,
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhX45X8OsYNoQJ0KVFkyhYsybNojpJ72rSl2mDUJ630wCHrY19KJYRBWeHoz9N5hD1XSWkllGqOrGiMvyXLaw4DCVzo9ptYjW1jByKSS21g0YMZpiIlpx2FSUgcvs_1F-MoUeTdzX6pJur9evb62fQMHaKZb5Z3IseO4vIb_Ta7vVuMU-8c=)
減掉平均數
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEiWCwrky6Af4np3YV9w6ic7yHV4oL1VB0uXklXtod994lBL84egDewJTgL0Kn-giYZV3vJ0jQEiU3mkuvpvelJJPIiNGwiUBYDP-ObsavMq1644alkD4SpSwpSCz3i0oGAIx1PL4LI2wRcV-MIMbNee_CqeXg78kpsftb6OeaYr0a_tdMuU=)
再除以標準差
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEh3nMxMicSMrZDxGa84FqWq4mhOwkM7NhHeOE9xZSYPoDFcKMP0CwgvSRvWY-bt6prBROq4ufm5ygEBR6RFvs9C2G4sV5M1eLGNfwZx8oekjg3l-jvLIQhkA6TyLtBLDXCaXOeZCr1CBzjhRNsUjiNoIcuvZZ2Nz1jcXVH6Y416j41jBsuB=)
,將會趨近平均數為0,標準差為1 的常態分佈(normal distribution)。或者是說當樣本數
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhU_Voo5qcmuZQltrWO4Kb83o4Nx01KJb59lG4clNsUsi2T9MQDaSbg60U01qTF8EDJgtS2viQopJ9Dk2EeGrf-U17Nwr5djFHUld9gWZKM0WrSB3ojiWLCx_ryT40oPKFAId8AxNhYpi7s8Sb05SzE3P5WLbWRPp5UaRJp67wABfr6Vy2Z=)
很大時,樣本和
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEgSTNCPHFdKBp7ecDzlo8HuLLEYHJ4M3yE_hqFVZyv5cd6QDuR_bH_tyr4CfOsaS17gMY9GR_aHferXz5oWmF8iUy8QjmJMk5uai6xv-6Ya24Svf-M3Zx0WEk11hiKXyCj9Nqi36pwuMsmvv9aByaEZTXbOO_sY2GlD7_6gEoJZ9wj0B2pV=)
減掉平均數
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEhtyFFZOz0BhF_MmmpNcW_7cGWskfdsiRhtUSb5Qp75c0w2wUd0_kp-wXTlXJYFTDjfCnspRkpUYF-yzRSbsgJqsakEAIANAFHBTtPfDKJw388uNKMDJj_5Qa6EmIm1iJEcAsSFCler0GpWkj4kBlMnzjZcys8npgiH6aCDlJwa6c5A282D=)
再除以標準差
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEjqT9-4VCYbhoQv5eGnZjq4sBAzJPyN3IV0lG5TEpcsI3tfLnPIEznNqVcg0rHcwhCfotsbViWV-w4wXw2anJoh394-AjK4QaWSkx-jYs9VH-grSR_y2SJbizMt-Ms8XVDTDQILZmTTZxaVMTiYXkFhyphenhyphenjPoF_f75J1KdLLN17QSLs92dFQc=)
,將會趨近平均數為0,標準差為1 的常態分佈,即
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEjIABezIp7_dR6U_Mpl4i4oJPDfdzZ1SNTOqzf251yWAcoMqeL_Csl-KZGRMnuTdvDVdLQ3y7MYAnqwzSpLVClEMbMi44w61-fp58cvsVYMlNibQsGTAsaGZf8MpN-SUddHSH6-iJcoQU3eFUZcULvVLPtbqqOkKD6hByfZ9Lz9NQ9X2EwZ=)
,或
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEj-OnPht664MKoGBK8xrUiWGEqdJcwgwHS1t_VNMn-dBUhDFfriK0ZvLrS4b42aCfwHaCu7z0UsUBe3Leqx4aw8F_XMxOEN1ndbWoTek_2iNHz0jPhoTywBmmp2nhHzcPw6iK2LQUoQrhhkb-Lqs7RuhdGHdttrss-A_zkCmpNLvSQDDtD3=)
, 所以
![](https://blogger.googleusercontent.com/img/proxy/AVvXsEj7geEBUmFjZyv70DUjjIVhdjQcSrpKW_vCk2K013kzags3Jkhad0xVMKoIY7Dh_8rRfHygvfO4lkUBJXBbeoZs-wzH8F7Zq_hr9vLJGlrsObO3tRB8SNq-eH_wSMEtDQnudUgiSX04aCapq3xmtphK0-WtcGXNhqS9LX6Di9cMlfNm77p_=)
的圖形看起來將會很像常態分佈的鐘形。
http://thchou.blogspot.tw/2008/09/hypothesis-testing.html?m=1
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