Formulas, Statistical Tables and R Commands: Statistical Tables
Table 1: Critical values z-distribution
Table 1a: left-sided #p#-values for negative values of #z#
\begin{eqnarray*} z&|&0.00&0.01&0.02&0.03&0.04&0.05&0.06&0.07&0.08&0.09\\ \hline -3.4&|&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0003&0.0002\\
-3.3&|&0.0005&0.0005&0.0005&0.0004&0.0004&0.0004&0.0004&0.0004&0.0004&0.0003\\
-3.2&|&0.0007&0.0007&0.0006&0.0006&0.0006&0.0006&0.0006&0.0005&0.0005&0.0005\\
-3.1&|&0.0010&0.0009&0.0009&0.0009&0.0008&0.0008&0.0008&0.0008&0.0007&0.0007\\
-3.0&|&0.0013&0.0013&0.0013&0.0012&0.0012&0.0011&0.0011&0.0011&0.0010&0.0010\\
-2.9&|&0.0019&0.0018&0.0018&0.0017&0.0016&0.0016&0.0015&0.0015&0.0014&0.0014\\
-2.8&|&0.0026&0.0025&0.0024&0.0023&0.0023&0.0022&0.0021&0.0021&0.0020&0.0019\\
-2.7&|&0.0035&0.0034&0.0033&0.0032&0.0031&0.0030&0.0029&0.0028&0.0027&0.0026\\
-2.6&|&0.0047&0.0045&0.0044&0.0043&0.0041&0.0040&0.0039&0.0038&0.0037&0.0036\\
-2.5&|&0.0062&0.0060&0.0059&0.0057&0.0055&0.0054&0.0052&0.0051&0.0049&0.0048\\
-2.4&|&0.0082&0.0080&0.0078&0.0075&0.0073&0.0071&0.0069&0.0068&0.0066&0.0064\\
-2.3&|&0.0107&0.0104&0.0102&0.0099&0.0096&0.0094&0.0091&0.0089&0.0087&0.0084\\
-2.2&|&0.0139&0.0136&0.0132&0.0129&0.0125&0.0122&0.0119&0.0116&0.0113&0.0110\\
-2.1&|&0.0179&0.0174&0.0170&0.0166&0.0162&0.0158&0.0154&0.0150&0.0146&0.0143\\
-2.0&|&0.0228&0.0222&0.0217&0.0212&0.0207&0.0202&0.0197&0.0192&0.0188&0.0183\\
-1.9&|&0.0287&0.0281&0.0274&0.0268&0.0262&0.0256&0.0250&0.0244&0.0239&0.0233\\
-1.8&|&0.0359&0.0351&0.0344&0.0336&0.0329&0.0322&0.0314&0.0307&0.0301&0.0294\\
-1.7&|&0.0446&0.0436&0.0427&0.0418&0.0409&0.0401&0.0392&0.0384&0.0375&0.0367\\
-1.6&|&0.0548&0.0537&0.0526&0.0516&0.0505&0.0495&0.0485&0.0475&0.0465&0.0455\\
-1.5&|&0.0668&0.0655&0.0643&0.0630&0.0618&0.0606&0.0594&0.0582&0.0571&0.0559\\
-1.4&|&0.0808&0.0793&0.0778&0.0764&0.0749&0.0735&0.0721&0.0708&0.0694&0.0681\\
-1.3&|&0.0968&0.0951&0.0934&0.0918&0.0901&0.0885&0.0869&0.0853&0.0838&0.0823\\
-1.2&|&0.1151&0.1131&0.1112&0.1093&0.1075&0.1056&0.1038&0.1020&0.1003&0.0985\\
-1.1&|&0.1357&0.1335&0.1314&0.1292&0.1271&0.1251&0.1230&0.1210&0.1190&0.1170\\
-1.0&|&0.1587&0.1562&0.1539&0.1515&0.1492&0.1469&0.1446&0.1423&0.1401&0.1379\\
-0.9&|&0.1841&0.1814&0.1788&0.1762&0.1736&0.1711&0.1685&0.1660&0.1635&0.1611\\
-0.8&|&0.2119&0.2090&0.2061&0.2033&0.2005&0.1977&0.1949&0.1922&0.1894&0.1867\\
-0.7&|&0.2420&0.2389&0.2358&0.2327&0.2296&0.2266&0.2236&0.2206&0.2177&0.2148\\
-0.6&|&0.2743&0.2709&0.2676&0.2643&0.2611&0.2578&0.2546&0.2514&0.2483&0.2451\\
-0.5&|&0.3085&0.3050&0.3015&0.2981&0.2946&0.2912&0.2877&0.2843&0.2810&0.2776\\
-0.4&|&0.3446&0.3409&0.3372&0.3336&0.3300&0.3264&0.3228&0.3192&0.3156&0.3121\\
-0.3&|&0.3821&0.3783&0.3745&0.3707&0.3669&0.3632&0.3594&0.3557&0.3520&0.3483\\
-0.2&|&0.4207&0.4168&0.4129&0.4090&0.4052&0.4013&0.3974&0.3936&0.3897&0.3859\\
-0.1&|&0.4602&0.4562&0.4522&0.4483&0.4443&0.4404&0.4364&0.4325&0.4286&0.4247\\
\ 0.0&|&0.5000&0.4960&0.4920&0.4880&0.4840&0.4801&0.4761&0.4721&0.4681&0.4641 \end{eqnarray*}
Table 1b: left-sided #p#-values for positive values of #z#
\begin{eqnarray*} z& |&0.00&0.01&0.02&0.03&0.04&0.05&0.06&0.07&0.08&0.09\\ \hline 0.0& |&0.5000&0.5040&0.5080&0.5120&0.5160&0.5199&0.5239&0.5279&0.5319&0.5359\\ 0.1& |&0.5398&0.5438&0.5478&0.5517&0.5557&0.5596&0.5636&0.5675&0.5714&0.5753\\ 0.2& |&0.5793&0.5832&0.5871&0.5910&0.5948&0.5987&0.6026&0.6064&0.6103&0.6141\\ 0.3& |&0.6179&0.6217&0.6255&0.6293&0.6331&0.6368&0.6406&0.6443&0.6480&0.6517\\ 0.4& |&0.6554&0.6591&0.6628&0.6664&0.6700&0.6736&0.6772&0.6808&0.6844&0.6879\\ 0.5& |&0.6915&0.6950&0.6985&0.7019&0.7054&0.7088&0.7123&0.7157&0.7190&0.7224\\ 0.6& |&0.7257&0.7291&0.7324&0.7357&0.7389&0.7422&0.7454&0.7486&0.7517&0.7549\\ 0.7& |&0.7580&0.7611&0.7642&0.7673&0.7704&0.7734&0.7764&0.7794&0.7823&0.7852\\ 0.8& |&0.7881&0.7910&0.7939&0.7967&0.7995&0.8023&0.8051&0.8078&0.8106&0.8133\\ 0.9& |&0.8159&0.8186&0.8212&0.8238&0.8264&0.8289&0.8315&0.8340&0.8365&0.8389\\ 1.0& |&0.8413&0.8438&0.8461&0.8485&0.8508&0.8531&0.8554&0.8577&0.8599&0.8621\\ 1.1& |&0.8643&0.8665&0.8686&0.8708&0.8729&0.8749&0.8770&0.8790&0.8810&0.8830\\ 1.2& |&0.8849&0.8869&0.8888&0.8907&0.8925&0.8944&0.8962&0.8980&0.8997&0.9015\\ 1.3& |&0.9032&0.9049&0.9066&0.9082&0.9099&0.9115&0.9131&0.9147&0.9162&0.9177\\ 1.4& |&0.9192&0.9207&0.9222&0.9236&0.9251&0.9265&0.9279&0.9292&0.9306&0.9319\\ 1.5& |&0.9332&0.9345&0.9357&0.9370&0.9382&0.9394&0.9406&0.9418&0.9429&0.9441\\ 1.6& |&0.9452&0.9463&0.9474&0.9484&0.9495&0.9505&0.9515&0.9525&0.9535&0.9545\\ 1.7& |&0.9554&0.9564&0.9573&0.9582&0.9591&0.9599&0.9608&0.9616&0.9625&0.9633\\ 1.8& |&0.9641&0.9649&0.9656&0.9664&0.9671&0.9678&0.9686&0.9693&0.9699&0.9706\\ 1.9& |&0.9713&0.9719&0.9726&0.9732&0.9738&0.9744&0.9750&0.9756&0.9761&0.9767\\ 2.0& |&0.9772&0.9778&0.9783&0.9788&0.9793&0.9798&0.9803&0.9808&0.9812&0.9817\\ 2.1& |&0.9821&0.9826&0.9830&0.9834&0.9838&0.9842&0.9846&0.9850&0.9854&0.9857\\ 2.2& |&0.9861&0.9864&0.9868&0.9871&0.9875&0.9878&0.9881&0.9884&0.9887&0.9890\\ 2.3& |&0.9893&0.9896&0.9898&0.9901&0.9904&0.9906&0.9909&0.9911&0.9913&0.9916\\ 2.4& |&0.9918&0.9920&0.9922&0.9925&0.9927&0.9929&0.9931&0.9932&0.9934&0.9936\\ 2.5& |&0.9938&0.9940&0.9941&0.9943&0.9945&0.9946&0.9948&0.9949&0.9951&0.9952\\ 2.6& |&0.9953&0.9955&0.9956&0.9957&0.9959&0.9960&0.9961&0.9962&0.9963&0.9964\\ 2.7& |&0.9965&0.9966&0.9967&0.9968&0.9969&0.9970&0.9971&0.9972&0.9973&0.9974\\ 2.8& |&0.9974&0.9975&0.9976&0.9977&0.9977&0.9978&0.9979&0.9979&0.9980&0.9981\\ 2.9& |&0.9981&0.9982&0.9982&0.9983&0.9984&0.9984&0.9985&0.9985&0.9986&0.9986\\ 3.0& |&0.9987&0.9987&0.9987&0.9988&0.9988&0.9989&0.9989&0.9989&0.9990&0.9990\\ 3.1& |&0.9990&0.9991&0.9991&0.9991&0.9992&0.9992&0.9992&0.9992&0.9993&0.9993\\ 3.2& |&0.9993&0.9993&0.9994&0.9994&0.9994&0.9994&0.9994&0.9995&0.9995&0.9995\\ 3.3& |&0.9995&0.9995&0.9995&0.9996&0.9996&0.9996&0.9996&0.9996&0.9996&0.9997\\ 3.4& |&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9997&0.9998 \end{eqnarray*}