{"id":73779,"date":"2016-08-29T07:26:49","date_gmt":"2016-08-28T23:26:49","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=73779"},"modified":"2021-10-06T16:03:57","modified_gmt":"2021-10-06T08:03:57","slug":"%e5%85%a9%e6%a8%a3%e6%9c%ac%e5%9d%87%e5%80%bc%e9%a1%af%e8%91%97%e6%80%a7%e6%aa%a2%e5%ae%9a%ef%bc%88%e4%b8%8a%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%85%a9%e6%a8%a3%e6%9c%ac%e5%9d%87%e5%80%bc%e9%a1%af%e8%91%97%e6%80%a7%e6%aa%a2%e5%ae%9a%ef%bc%88%e4%b8%8a%ef%bc%89\/","title":{"rendered":"\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0a\uff09"},"content":{"rendered":"

\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0a\uff09(T Test for Two Sample Means (I))<\/strong><\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u8fb2\u85dd\u5b78\u7cfb \u9ec3\u7e95\u6dc7<\/strong><\/span><\/p>\n

\u4e00\u3001\u524d\u8a00<\/span><\/strong><\/p>\n

\u672c\u7bc7\u5c07\u4ecb\u7d39\u5169\u6a23\u672c\u65bc\u4e0d\u540c\u60c5\u6cc1\u6642\u7684\u5e73\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff0c\u4f8b\u5982\u6211\u5011\u60f3\u8981\u4e86\u89e3\u6bcf\u500b\u4eba\u5de6\u53f3\u624b\u7684\u5e73\u5747\u8840\u58d3\u662f\u5426\u4e0d\u540c\uff0c\u6216\u8005\u5169\u7a2e\u4e0d\u540c\u5b30\u5152\u5976\u7c89\u914d\u65b9\u5c0d\u65bc\u5b30\u5152\u5e73\u5747\u9ad4\u91cd\u589e\u52a0\u662f\u5426\u6703\u6709\u5f71\u97ff\u6642\uff0c\u61c9\u8a72\u9078\u7528\u7684\u7d71\u8a08\u6aa2\u5b9a\u6cd5\u3002<\/p>\n

\u4e8c\u3001\u7368\u7acb\u6a23\u672c\u8207\u6210\u5c0d\u6a23\u672c\u5dee\u7570<\/span><\/strong><\/p>\n

\u8aaa\u660e\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\u4e4b\u524d\uff0c\u5148\u4f86\u4ecb\u7d39\u6a23\u672c\u7684\u5169\u7a2e\u4e0d\u540c\u578b\u614b\u2014\u300c\u7368\u7acb\u6a23\u672c\u300d\u8207\u300c\u6210\u5c0d\u6a23\u672c\u300d\uff0c\u4e0d\u540c\u6a23\u672c\u578b\u614b\u9078\u64c7\u4e0d\u540c\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\u3002\u7368\u7acb\u6a23\u672c\u70ba\u4e0d\u540c\u8a66\u9a57\u55ae\u4f4d\u6240\u5f97\u5230\u4e4b\u89c0\u6e2c\u503c\uff0c\u4f8b\u5982\u5169\u7a2e\u4e0d\u540c\u914d\u65b9\u5b30\u5152\u5976\u7c89\u5c0d\u65bc\u5b30\u5152\u9ad4\u91cd\u589e\u52a0\u4e4b\u5f71\u97ff\uff0c\u5403 A \u914d\u65b9\u5b30\u5152\u5976\u7c89\u7684\u5b30\u5152\u8207\u5403 B \u914d\u65b9\u5b30\u5152\u5976\u7c89\u7684\u5b30\u5152\u662f\u4e0d\u540c\u7684\uff0c\u63db\u53e5\u8a71\u8aaa\uff0c\u5403 A \u914d\u65b9\u5b30\u5152\u5976\u7c89\u7684\u5b30\u5152\u9ad4\u91cd\u589e\u52a0\u4e4b\u89c0\u6e2c\u503c\u8207\u5403 B \u914d\u65b9\u5b30\u5152\u5976\u7c89\u7684\u5b30\u5152\u9ad4\u91cd\u589e\u52a0\u4e4b\u89c0\u6e2c\u503c\u662f\u7121\u95dc\u4e14\u4e92\u4e0d\u76f8\u5f71\u97ff\uff0c\u5176\u7a31\u505a\u7368\u7acb\u6a23\u672c\uff1b\u6210\u5c0d\u6a23\u672c\u70ba\u540c\u4e00\u8a66\u9a57\u55ae\u4f4d\u65bc\u4e0d\u540c\u74b0\u5883\u6240\u5f97\u5230\u4e4b\u89c0\u6e2c\u503c\uff0c\u8209\u4f8b\u4f86\u8aaa\uff0c10 \u540d\u6d17\u814e\u75c5\u60a3\u900f\u6790\u524d\u5f8c\u9ad4\u91cd\u4e4b\u8b8a\u5316\uff0c\u540c\u4e00\u4f4d\u75c5\u60a3\u900f\u6790\u524d\u5f8c\u4e4b\u9ad4\u91cd\u5747\u6e2c\u91cf\u81ea\u540c\u4e00\u4eba\uff0c\u8868\u793a 10 \u540d\u6d17\u814e\u75c5\u60a3\u900f\u6790\u524d\u4e4b\u9ad4\u91cd\u8207\u900f\u6790\u5f8c\u4e4b\u9ad4\u91cd\u662f\u76f8\u95dc\u4e14\u914d\u5c0d\u7684\u89c0\u6e2c\u503c\uff0c\u5176\u8b02\u4e4b\u70ba\u6210\u5c0d\u6a23\u672c\u3002<\/p>\n

\u4e09\u3001\u5169\u6bcd\u7fa4\u9ad4\u5e73\u5747\u503c\u5dee\u7684\u5047\u8a2d\u6aa2\u5b9a<\/span><\/strong><\/p>\n

1.\u6bcd\u7fa4\u9ad4\u70ba\u5e38\u614b\u5206\u5e03\u4e14\u8b8a\u7570\u6578\u5df2\u77e5<\/span><\/strong><\/p>\n

\u7576\u6211\u5011\u53d6\u5f97\u5169\u7b46\u4e0d\u540c\u96a8\u6a5f\u7368\u7acb\u6a23\u672c\u8cc7\u6599\uff0c\u6b64\u5169\u7b46\u7368\u7acb\u6a23\u672c\u81ea\u5169\u6bcd\u7fa4\u9ad4\u62bd\u6a23\u7372\u5f97\uff0c\u4e14\u5169\u6bcd\u7fa4\u9ad4\u90fd\u70ba\u5e38\u614b\u5206\u5e03\u4e14\u8b8a\u7570\u6578\u5df2\u77e5\u70ba \\(\\sigma^2_1\\) \u8207 \\(\\sigma^2_2\\) \u6642\uff0c\u53ef\u4ee5\u4f7f\u7528\u7d71\u8a08\u91cf\uff1a<\/p>\n

\\(\\displaystyle Z=\\frac{|\\overline{x}_1-\\overline{x}_2|}{\\sqrt{\\frac{\\sigma^2_1}{n_1}+\\frac{\\sigma^2_2}{n_2}}}~~~~~~~~~(1)\\)<\/p>\n

\u6aa2\u5b9a\u5169\u6a23\u672c\u7684\u5747\u503c\u662f\u5426\u76f8\u540c\uff0c\u800c \\((1)\\) \u5f0f\u4e2d\u7684 \\(\\overline{x}_1\\)\u3001\\(\\overline{x}_2\\) \u70ba\u6b64\u5169\u7b46\u6a23\u672c\u4e4b\u5e73\u5747\u503c\uff0c\\(n_1\\)\u3001\\(n_2\\) \u5247\u662f\u5169\u7d44\u6a23\u672c\u62bd\u6a23\u7684\u6a23\u672c\u6578\u3002\u4f8b\u5982\uff1a\u6b32\u6aa2\u5b9a\u67d0\u4e00\u516c\u53f8\u7537\u8077\u54e1\u8207\u5973\u8077\u54e1\u5de5\u4f5c\u6642\u6578\u662f\u5426\u76f8\u540c\uff0c\u56e0\u6b64\u7531\u516c\u53f8\u8077\u54e1\u540d\u55ae\u96a8\u6a5f\u62bd\u53d6 50 \u540d\u7537\u8077\u54e1\u548c 100 \u540d\u5973\u8077\u54e1\uff0c\u5206\u5225\u8a18\u9304\u6bcf\u540d\u8077\u54e1\u5de5\u4f5c\u6642\u6578\uff0c\u4e26\u8a08\u7b97\u5169\u7b46\u96a8\u6a5f\u6a23\u672c\u5e73\u5747\u503c\u5206\u5225\u7537\u8077\u54e1\u5e73\u5747\u4e0a\u73ed\u6642\u6578 5.5 \u5c0f\u6642 \\((\\overline{x}_1)\\) \u8207\u5973\u8077\u54e1\u5e73\u5747\u4e0a\u73ed\u6642\u6578 5.3 \u5c0f\u6642 \\((\\overline{x}_2)\\)\uff0c\u800c\u7814\u7a76\u8005\u5728\u4e8b\u524d\u5df2\u77e5\u5169\u6bcd\u9ad4\u8b8a\u7570\u6578\u5206\u5225 \\(\\sigma^2_1\\) \u70ba \\(0.4^2\\)\u3001\\(\\sigma^2_2\\) \u70ba \\(0.3^2\\)\uff0c\u5247\u8a08\u7b97\u51fa\u4f86\u7684:<\/p>\n

\\(\\displaystyle Z=\\frac{|5.5-5.3|}{\\sqrt{\\frac{0.4^2}{50}+\\frac{0.3^2}{100}}}=3.123\\)<\/p>\n

\u70ba\u4e86\u4e86\u89e3\u5728\u6b64\u6a23\u672c\u689d\u4ef6\u4e0b 0.2 \u5c0f\u6642\u7684\u5dee\u7570\u662f\u5426\u5920\u986f\u8457\uff0c\u6211\u5011\u5c07\u900f\u904e\u5224\u5b9a\u8a08\u7b97\u51fa\u7684 Z \u503c\u5927\u5c0f\u4f86\u6c7a\u5b9a\u3002\u9996\u5148\u9650\u5b9a\u4e00\u500b\u5408\u7406\u7684\u81e8\u754c Z \u503c\uff0c\u5982\u679c\u5169\u6a23\u672c\u5dee\u7570\u5c0f\u65bc\u9019\u500b\u81e8\u754c\u503c\uff0c\u6211\u5011\u5c31\u8a8d\u5b9a\u5169\u6a23\u672c\u4e4b\u5747\u503c\u76f8\u540c\u3002\u6b64\u81e8\u754c\u503c\u6211\u5011\u901a\u5e38\u8a2d\u5b9a\u70ba \\(Z_{0.025}=1.96\\)\uff0c\u9019\u500b\u6578\u5b57\u662f\u6a19\u6e96\u5e38\u614b\u5206\u5e03\u7684 97.5% \u767e\u5206\u4f4d\u6578\u3002\u5728\u7537\u8077\u54e1\u8207\u5973\u8077\u54e1\u5de5\u4f5c\u6642\u6578\u7684\u7bc4\u4f8b\u4e2d\uff0c\u7531\u65bc Z > 1.96\uff0c\u986f\u793a\u7537\u8077\u54e1\u8207\u5973\u8077\u54e1\u5de5\u4f5c\u6642\u6578\u5747\u503c\u5177\u6709\u986f\u8457\u5dee\u7570\u3002<\/p>\n

2.\u5169\u6bcd\u7fa4\u9ad4\u70ba\u5e38\u614b\u5206\u5e03\u4e14\u6bcd\u9ad4\u8b8a\u7570\u6578\u672a\u77e5<\/span><\/strong><\/p>\n

\\((\\text{I})\\)\u00a0\u5047\u8a2d\u5169\u6bcd\u7fa4\u9ad4\u8b8a\u7570\u6578\u672a\u77e5\u4f46\u76f8\u7b49\u6642 \\((\\sigma^2_1=\\sigma^2_2=\\sigma^2)\\)<\/p>\n

\u7576\u6211\u5011\u53d6\u5f97\u5169\u7b46\u4e0d\u540c\u96a8\u6a5f\u7368\u7acb\u6a23\u672c\u8cc7\u6599\uff0c\u6b64\u5169\u7b46\u7368\u7acb\u6a23\u672c\u81ea\u5169\u6bcd\u7fa4\u9ad4\u62bd\u6a23\u7372\u5f97\uff0c\u4e14\u5169\u6bcd\u7fa4\u9ad4\u90fd\u70ba\u5e38\u614b\u5206\u5e03\u4e14\u8b8a\u7570\u6578\u672a\u77e5\u4f46\u76f8\u540c\u6642\uff0c\u53ef\u904b\u7528\u7684\u7d71\u8a08\u91cf\u70ba\uff1a<\/p>\n

\\(\\displaystyle t=\\frac{|\\overline{x}_1-\\overline{x}_2|}{\\sqrt{\\frac{S^2_p}{n_1}+\\frac{S^2_p}{n_2}}}=\\frac{|\\overline{x}_1-\\overline{x}_2|}{\\sqrt{S^2_p\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}},~~~S^2_p=\\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2}~~~~~~(2)\\)<\/p>\n

\\((2)\\) \u5f0f\u85c9\u7531\u5408\u4f75\u5169\u500b\u6a23\u672c\u8b8a\u7570\u6578 \\(S^2_1\\) \u8207 \u00a0\\(S^2_2\\) \u4f86\u4f30\u8a08\u5171\u540c\u8b8a\u7570\u6578 \\(\\sigma^2\\)\uff0c\u4ee5 \\(S^2_p\\) \u8868\u793a\u4e4b\uff0c\\(n_1\\)\u3001\\(n_2\\) \u5247\u662f\u5169\u7d44\u6a23\u672c\u62bd\u6a23\u7684\u6a23\u672c\u6578\u3002\u8209\u4f8b\u4f86\u8aaa\uff0c\u6b32\u6bd4\u8f03\u5169\u6240\u5927\u5b78\u5b78\u751f\u7684\u8eab\u9ad8\u5747\u503c\u662f\u5426\u76f8\u540c\uff0c\u4eca\u7531 A \u5927\u5b78\u62bd\u51fa 16 \u4f4d\u5b78\u751f\uff0c\u6e2c\u91cf\u5e73\u5747\u8eab\u9ad8\u70ba 172 \u516c\u5206 \\((\\overline{x}_1)\\)\uff0c\u6a19\u6e96\u5dee\u70ba 8.45 \u516c\u5206 \\((S^2_1)\\)\uff1bB \u5927\u5b78\u4e5f\u62bd\u51fa 16 \u4f4d\u5b78\u751f\uff0c\u5e73\u5747\u8eab\u9ad8\u70ba 168 \u516c\u5206 \\((\\overline{x}_2)\\)\uff0c\u6a19\u6e96\u5dee\u70ba 7.8 \u516c\u5206 \\((S^2_2)\\)\u3002\u5047\u82e5 A\u3001B \u5169\u5927\u5b78\u5b78\u751f\u8eab\u9ad8\u4e4b\u6bcd\u7fa4\u9ad4\u5206\u5e03\u70ba\u5e38\u614b\u5206\u5e03\uff0c\u800c\u4e14\u8b8a\u7570\u6578\u76f8\u540c\u3002\u7531\u65bc\u5169\u6bcd\u7fa4\u9ad4\u8b8a\u7570\u6578\u76f8\u540c\uff0c\u56e0\u6b64\u9700\u8981\u5148\u8a08\u7b97\u6a23\u672c\u5171\u540c\u8b8a\u7570\u6578 \\(S^2_p\\)\uff1a<\/p>\n

\\(\\displaystyle S^2_p=\\frac{(16-1)8.45^2+(16-1)7.8^2}{16+16-2}=66.12\\)<\/p>\n

\u5f97\u5230 \\(S^2_p\\) \u5f8c\uff0c\u5247\u8a08\u7b97\u51fa\u4f86\u7684:<\/p>\n

\\(\\displaystyle t=\\frac{|172-168|}{\\sqrt{66.12(\\frac{1}{16}+\\frac{1}{16})}}=1.39\\)<\/p>\n

\u60f3\u8981\u77e5\u9053\u5728\u6b64\u689d\u4ef6\u4e0b\uff0c4 \u516c\u5206\u7684\u5dee\u7570\u5920\u4e0d\u5920\u986f\u8457\uff1f\u53ef\u4ee5\u5c07\u7d71\u8a08\u91cf \\(t\\) \u8207 \\(t_{0.025,n_1+n_2-2}=\\) \u81ea\u7531\u5ea6\u70ba \\(n_1+n_2-2\\) \u7684 t \u5206\u5e03\u7684 97.5% \u767e\u5206\u4f4d\u6578\u6bd4\u8f03\uff0c\u8a72\u6578\u503c\u53ef\u4ee5\u5229\u7528 Excel \u7684 T.INV \u51fd\u5f0f\u53d6\u5f97\u3002\u65bc\u6b64\u8eab\u9ad8\u4f8b\u5b50\u4e2d\uff0c\u7531\u65bc \\(t < t_{0.025,30}=2.04\\)\uff0c\u8868\u793a\u5169\u5927\u5b78\u5b78\u751f\u4e4b\u8eab\u9ad8\u7121\u986f\u8457\u5dee\u7570\u3002<\/p>\n

\"73779_p1\"<\/a>

\u5716\u4e00\u3001\u5169\u6bcd\u7fa4\u9ad4\u5e73\u5747\u503c\u5dee\u7684\u5047\u8a2d\u6aa2\u5b9a\uff08\u5047\u8a2d\u5169\u6bcd\u7fa4\u9ad4\u8b8a\u7570\u6578\u672a\u77e5\u4f46\u76f8\u7b49\uff09\u3002\uff08\u672c\u6587\u4f5c\u8005\u9ec3\u7e95\u6dc7\u7e6a\u88fd\uff09<\/p><\/div>\n

\u9023\u7d50\uff1a\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0b\uff09<\/a><\/p>\n

\n

\u53c3\u8003\u6587\u737b<\/strong><\/p>\n

    \n
  1. \u6c88\u660e\u4f86 (2014)\u3002\u751f\u7269\u7d71\u8a08\u5b78\u5165\u9580\u3002\u4e5d\u5dde\u3002<\/li>\n
  2. \u90ed\u5bf6\u931a\u3001\u9673\u7389\u654f (2011)\u3002\u751f\u7269\u7d71\u8a08\u5b78\u3002\u4e94\u5357\u3002<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0a\uff09(T Test for Two Sample Means (I)) \u570b\u7acb\u81fa\u7063\u5927\u5b78\u8fb2\u85dd…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,230,229],"tags":[10581,10463,10582,10027,10462,11064,10580],"class_list":["post-73779","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math06-01","category-math06","tag-independent-sample","tag-paired-sample","tag-sd","tag-standard-deviation","tag-10462","tag-11064","tag-10580","loop-entry","cat-111","cat-230","cat-229","no-thumbnail"],"views":9517,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73779","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=73779"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73779\/revisions"}],"predecessor-version":[{"id":85991,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73779\/revisions\/85991"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=73779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=73779"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=73779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}