{"id":1625,"date":"2023-07-25T14:55:46","date_gmt":"2023-07-25T14:55:46","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%a6%e0%a5%8d%e0%a4%b5%e0%a4%bf%e0%a4%aa%e0%a4%a6-%e0%a4%86%e0%a4%a4%e0%a5%8d%e0%a4%ae%e0%a4%b5%e0%a4%bf%e0%a4%b6%e0%a5%8d%e0%a4%b5%e0%a4%be%e0%a4%b8-%e0%a4%85%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%be\/"},"modified":"2023-07-25T14:55:46","modified_gmt":"2023-07-25T14:55:46","slug":"%e0%a4%a6%e0%a5%8d%e0%a4%b5%e0%a4%bf%e0%a4%aa%e0%a4%a6-%e0%a4%86%e0%a4%a4%e0%a5%8d%e0%a4%ae%e0%a4%b5%e0%a4%bf%e0%a4%b6%e0%a5%8d%e0%a4%b5%e0%a4%be%e0%a4%b8-%e0%a4%85%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%be","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%a6%e0%a5%8d%e0%a4%b5%e0%a4%bf%e0%a4%aa%e0%a4%a6-%e0%a4%86%e0%a4%a4%e0%a5%8d%e0%a4%ae%e0%a4%b5%e0%a4%bf%e0%a4%b6%e0%a5%8d%e0%a4%b5%e0%a4%be%e0%a4%b8-%e0%a4%85%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%be\/","title":{"rendered":"\u0906\u0930 \u092e\u0947\u0902 \u0926\u094d\u0935\u093f\u092a\u0926 \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u0926\u094d\u0935\u093f\u092a\u0926 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940<\/strong> \u0917\u0923\u0928\u093e \u0928\u093f\u092e\u094d\u0928 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 = p<\/strong> <strong>+\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u094b\u0928\u093e:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u092a\u0940:<\/strong> &#8220;\u0938\u092b\u0932\u0924\u093e\u0913\u0902&#8221; \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> \u091a\u0941\u0928\u093e \u0939\u0941\u0906 z \u092e\u093e\u0928<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0906\u092a\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u093e z \u092e\u093e\u0928 \u0906\u092a\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u091a\u0941\u0928\u0947 \u0917\u090f \u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0915\u0947 \u0938\u094d\u0924\u0930 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0928\u093f\u092e\u094d\u0928 \u0924\u093e\u0932\u093f\u0915\u093e z \u092e\u093e\u0928 \u0926\u093f\u0916\u093e\u0924\u0940 \u0939\u0948 \u091c\u094b \u0938\u092c\u0938\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0938\u094d\u0924\u0930 \u0935\u093f\u0915\u0932\u094d\u092a\u094b\u0902 \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u0940 \u0939\u0948:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>\u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0915\u093e \u090f\u0915 \u0938\u094d\u0924\u0930<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>z \u092e\u093e\u0928<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.90<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1,645<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.95<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1.96<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.99<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2.58<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \u0939\u092e \u0915\u093f\u0938\u0940 \u0915\u093e\u0909\u0902\u091f\u0940 \u092e\u0947\u0902 \u0909\u0928 \u0928\u093f\u0935\u093e\u0938\u093f\u092f\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0932\u0917\u093e\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u090f\u0915 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u093e\u0928\u0942\u0928 \u0915\u093e \u0938\u092e\u0930\u094d\u0925\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0939\u092e 100 \u0928\u093f\u0935\u093e\u0938\u093f\u092f\u094b\u0902 \u0915\u093e \u090f\u0915 \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u0928\u092e\u0942\u0928\u093e \u091a\u0941\u0928\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 56 \u0915\u093e\u0928\u0942\u0928 \u0915\u0947 \u092a\u0915\u094d\u0937 \u092e\u0947\u0902 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p style=\"text-align: left;\"> <span style=\"color: #000000;\">\u092f\u0939 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u0915\u093e\u0928\u0942\u0928 \u0915\u093e \u0938\u092e\u0930\u094d\u0925\u0928 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0915\u093e\u0909\u0902\u091f\u0940\u0935\u094d\u092f\u093e\u092a\u0940 \u0928\u093f\u0935\u093e\u0938\u093f\u092f\u094b\u0902 \u0915\u0947 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0924\u0940\u0928 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0924\u0930\u0940\u0915\u094b\u0902 \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u0935\u093f\u0927\u093f 1: \u092a\u094d\u0930\u094b\u092a.\u091f\u0947\u0938\u094d\u091f() \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u0926\u094d\u0935\u093f\u092a\u0926 95% \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u090f\u0915 \u0924\u0930\u0940\u0915\u093e \u092c\u0947\u0938 \u0906\u0930 \u092e\u0947\u0902 <strong>\u092a\u094d\u0930\u094b\u092a.\u091f\u0947\u0938\u094d\u091f()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0939\u0948:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate 95% confidence interval\n<\/span>prop. <span style=\"color: #3366ff;\">test<\/span> (x=56, n=100, conf. <span style=\"color: #3366ff;\">level<\/span> =.95, correct= <span style=\"color: #008000;\">FALSE<\/span> )\n\n\n\t1-sample proportions test without continuity correction\n\ndata: 56 out of 100, null probability 0.5\nX-squared = 1.44, df = 1, p-value = 0.2301\nalternative hypothesis: true p is not equal to 0.5\n95 percent confidence interval:\n 0.4622810 0.6532797\nsample estimates:\n   p \n0.56 \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0915\u093e\u0928\u0942\u0928 \u0915\u093e \u0938\u092e\u0930\u094d\u0925\u0928 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u0915\u093e\u0909\u0902\u091f\u0940 \u0928\u093f\u0935\u093e\u0938\u093f\u092f\u094b\u0902 \u0915\u0947 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f 95% \u0938\u0940\u0906\u0908 <strong>[.46228, .65328]<\/strong> \u0939\u0948\u0964<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u0935\u093f\u0927\u093f 2: \u092c\u093f\u0928\u0915\u0949\u0928\u094d\u092b() \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u0915\u0949\u0928\u094d\u092b\u093f\u0921\u0947\u0902\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u0926\u0942\u0938\u0930\u093e \u0924\u0930\u0940\u0915\u093e <strong>Hmisc<\/strong> \u092a\u0948\u0915\u0947\u091c \u0938\u0947 <strong>binconf()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0939\u0948:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #993300;\">library<\/span> (Hmisc)<\/span>\n\n#calculate 95% confidence interval\n<\/span>binconf(x=56, n=100, alpha=.05)\n\n PointEast Lower Upper\n     0.56 0.462281 0.6532797\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u092f\u0939 \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u092a\u093f\u091b\u0932\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902 \u0917\u0923\u0928\u093e \u0915\u0940 \u0917\u0908 \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0935\u093f\u0927\u093f 3: \u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u092e\u0948\u0928\u094d\u092f\u0941\u0905\u0932 \u0930\u0942\u092a \u0938\u0947 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0906\u0930 \u092e\u0947\u0902 \u0926\u094d\u0935\u093f\u092a\u0926 95% \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u0926\u0942\u0938\u0930\u093e \u0924\u0930\u0940\u0915\u093e \u0907\u0938\u0947 \u092e\u0948\u0928\u094d\u092f\u0941\u0905\u0932 \u0930\u0942\u092a \u0938\u0947 \u0915\u0930\u0928\u093e \u0939\u0948:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define proportion\n<\/span>p &lt;- 56\/100\n\n<span style=\"color: #008080;\">#define significance level\n<\/span>a &lt;- .05\n\n<span style=\"color: #008080;\">#calculate 95% confidence interval\n<\/span>p + c(- <span style=\"color: #3366ff;\">qnorm<\/span> (1-a\/2), <span style=\"color: #3366ff;\">qnorm<\/span> (1-a\/2))* <span style=\"color: #3366ff;\">sqrt<\/span> ((1\/100)*p*(1-p))\n\n[1] 0.4627099 0.6572901<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u092f\u0939\u093e\u0902 <strong>qnorm()<\/strong> \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u091c\u093e\u0928\u0947\u0902: <a href=\"https:\/\/statorials.org\/hi\/\u0906\u0930-\u092e\u0947\u0902-\u0921\u0940\u0928\u0949\u0930\u094d\u092e-\u092a\u094b\u0928\u0949\u0930\u094d\u092e-\u0906\u0930\u0928\u0949\u0930\u094d\u092e-\u0915\u094d\u092f\u0942\u0928\u0949\u0930\u094d\u092e\/\">R \u092e\u0947\u0902 dnorm, pnorm, qnorm \u0914\u0930 rnorm \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0917\u093e\u0907\u0921<\/a><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0938\u0902\u0938\u093e\u0927\u0928<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/hi\/\u0926\u094d\u0935\u093f\u092a\u0926-\u092a\u0930\u0940\u0915\u094d\u0937\u0923-\u0906\u0930\/\" target=\"_blank\" rel=\"noopener\">\u0906\u0930 \u092e\u0947\u0902 \u0926\u094d\u0935\u093f\u092a\u0926 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902<\/a><br \/> <a href=\"https:\/\/statorials.org\/hi\/\u0926\u094d\u0935\u093f\u092a\u0926-\u092c\u0902\u091f\u0928-r-\u0906\u0932\u0947\u0916\u093f\u0924-\u0915\u0930\u0947\u0902\/\" target=\"_blank\" rel=\"noopener\">R \u092e\u0947\u0902 \u0926\u094d\u0935\u093f\u092a\u0926 \u092c\u0902\u091f\u0928 \u0915\u0948\u0938\u0947 \u0906\u0932\u0947\u0916\u093f\u0924 \u0915\u0930\u0947\u0902<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0926\u094d\u0935\u093f\u092a\u0926 \u0938\u0902\u092d\u093e\u0935\u094d\u092f\u0924\u093e \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0940 \u0917\u0923\u0928\u093e \u0928\u093f\u092e\u094d\u0928 \u0938\u0942\u0924\u094d\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948: \u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 = p +\/- z*(\u221a p(1-p) \/ n ) \u0938\u094b\u0928\u093e: \u092a\u0940: &#8220;\u0938\u092b\u0932\u0924\u093e\u0913\u0902&#8221; \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 z: \u091a\u0941\u0928\u093e \u0939\u0941\u0906 z \u092e\u093e\u0928 n: \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 \u0906\u092a\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u093e z \u092e\u093e\u0928 \u0906\u092a\u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u091a\u0941\u0928\u0947 \u0917\u090f \u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0915\u0947 \u0938\u094d\u0924\u0930 \u092a\u0930 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