r r Table 4 Biomial Probability Distributio C, r p q This table shows the probability of r successes i idepedet trials, each with probability of success p. p r.01.05.10.15.0.5.30.35.40.45.50.55.60.65.70.75.80.85.90.95 0.980.90.810.73.640.563.490.43.360.303.50.03.160.13.090.063.040.03.010.00 1.00.095.180.55.30.375.40.455.480.495.500.495.480.455.40.375.30.55.180.095.000.00.010.03.040.063.090.13.160.03.50.303.360.43.490.563.640.73.810.90 3 0.970.857.79.614.51.4.343.75.16.166.15.091.064.043.07.016.008.003.001.000 1.09.135.43.35.384.4.441.444.43.408.375.334.88.39.189.141.096.057.07.007.000.007.07.057.096.141.189.39.88.334.375.408.43.444.441.4.384.35.43.135 3.000.000.001.003.008.016.07.043.064.091.15.166.16.75.343.4.51.614.79.857 4 0.961.815.656.5.410.316.40.179.130.09.06.041.06.015.008.004.00.001.000.000 1.039.171.9.368.410.4.41.384.346.300.50.00.154.11.076.047.06.011.004.000.001.014.049.098.154.11.65.311.346.368.375.368.346.311.65.11.154.098.049.014 3.000.000.004.011.06.047.076.11.154.00.50.300.346.384.41.4.410.368.9.171 4.000.000.000.001.00.004.008.015.06.041.06.09.130.179.40.316.410.5.656.815 5 0.951.774.590.444.38.37.168.116.078.050.031.019.010.005.00.001.000.000.000.000 1.048.04.38.39.410.396.360.31.59.06.156.113.077.049.08.015.006.00.000.000.001.01.073.138.05.64.309.336.346.337.31.76.30.181.13.088.051.04.008.001 3.000.001.008.04.051.088.13.181.30.76.31.337.346.336.309.64.05.138.073.01 4.000.000.000.00.006.015.08.049.077.113.156.06.59.31.360.396.410.39.38.04 5.000.000.000.000.000.001.00.005.010.019.031.050.078.116.168.37.38.444.590.774 6 0.941.735.531.377.6.178.118.075.047.08.016.008.004.00.001.000.000.000.000.000 1.057.3.354.399.393.356.303.44.187.136.094.061.037.00.010.004.00.000.000.000.001.031.098.176.46.97.34.38.311.78.34.186.138.095.060.033.015.006.001.000 3.000.00.015.04.08.13.185.36.76.303.31.303.76.36.185.13.08.04.015.00 4.000.000.001.006.015.033.060.095.138.186.34.78.311.38.34.97.46.176.098.031 5.000.000.000.000.00.004.010.00.037.061.094.136.187.44.303.356.393.399.354.3 6.000.000.000.000.000.000.001.00.004.008.016.08.047.075.118.178.6.377.531.735 7 0.93.698.478.31.10.133.08.049.08.015.008.004.00.001.000.000.000.000.000.000 1.066.57.37.396.367.311.47.185.131.087.055.03.017.008.004.001.000.000.000.000.00.041.14.10.75.311.318.99.61.14.164.117.077.047.05.01.004.001.000.000 3.000.004.03.06.115.173.7.68.90.9.73.39.194.144.097.058.09.011.003.000 4.000.000.003.011.09.058.097.144.194.39.73.9.90 ;68.7.173.115.06.03.004 5.000.000.000.001.004.01.05.047.077.117.164.14.61.99.318.311.75.10.14.041 6.000.000.000.000.000.001.004.008.017.03.055.087.131.185.47.311.367.396.37.57 7.000.000.000.000.000.000.000.001.00.004.008.015.08.049.08.133.10.31.478.698
Table 4 cotiued p r.01.05.10.15.0.5.30.35.40.45.50.55.60.65.70.75.80.85.90.95 8 0.93.663.430.7.168.100.058.03.017.008.004.00.001.000.000.000.000.000.000.000 1.075.79.383.385.336.67.198.137.090.055.031.016.008.003.001.000.000.000.000.000.003.051.149.38.94.311.96.59.09.157.109.070.041.0.010.004.001.000.000.000 3.000.005.033.084.147.08.54.79.79.57.19.17.14.081.047.03.009.003.000.000 4.000.000.005 :018.046.087.136.188.3.63.73.63.3.188.136.087.046.018.005.000 5.000.000.000.003.009.03.047.081.14.17.19.57.79.79.54.08.147.084.033.005 6.000.000.000.000.001.004.010.0.041.070.109.157.09.59.96.311.94.38.149.051 7.000.000.000.000.000.000.001.003.008.016.031.055.090.137.198.67.336.385.383.79 8.000.000.000.000.000 000.000.000.001.00.004.008.017.03.058.100.168.7.430.663 9 0.914.630.387.3.134.075.040.01.010.005.00.001.000.000.000.000.000.000.000.000 1.083.99.387.368.30.5.156.100.060.034.018.008.004.001.000.000.000.000.000.000.003.063.17.60.30.300.67.16.161.111.070.041.01.010.004.001.000.000.000.000 3.000.008.045.107.176.34.67.7.51.1.164.116.074.04.01.009.003.001.000.000 4.000.001.007.08.066.117.17.19.51.60.46.13.167.118.074.039.017.005.001.000 5.000.000.001.005.017.039.074.118.167.13.46.60.51.19.17.117.066.08.007.001 6.000.000.000.001.003.009.01.04.074.116.164.1.51.7.67.34.176.107.045.008 7.000.000.000.000.000.001.004.010.01.041.070.111.161.16.67.300.30.60.17.063 8.000.000.000.000.000.000.000.001.004.008.018.034.060.100.156.5.30.368.387.99 9.000.000.000.000.000.000.000.000.000.001.00.005.010.01.040.075.134.3.387.630 10 0.904.599.349.197.107.056.08.014.006.003.001.000.000.000.000.000.000.000.000.000 1.091.315.387.347.68.188.11.07.040.01.010.004.00.000.000.000.000.000.000.000.004.075.194.76.30.8.33.176.11.076.044.03.011.004.001.000.000.000.000.000 3.000.010.057.130.01.50.67.5.15.166.117.075.04.01.009.003.001.000.000.000 4.000.001.011.040.088.146.00.38.51.38.05.160.111.069.037.016.006.001.000.000 5.000.000.001.008.06.058.103.154.01.34.46.34.01.154.103.058.06.008.001.000 6.000.000.000.001.006.016.037.069.111.160.05.38.51.38.00.146.088.040.011.001 7.000.000.000.000.001.003.009.01.04.075.117.166.15.5.67.50.01.130.057.010 8.000.000.000.000.000.000.001.004.011.03.044.076.11.176.33.8.30.76.194.07. 9.000.000.000.000.000.000.000.000.00.004.010.01.040.07.11.188.68.347.387.315 10.000.000.000.000.000.000.000.000.000.000.001.003.006.014.08.056.107.197.349.599 11 0.895.569.314.167.086.04.00.009.004.001.000.000.000.000.000.000.000.000.000.000 1.099.39.384.35.36.155.093.05.07.013.005.00.001.000.000.000.000.000.000.000.005.087.13.87.95.58.00.140.089.051.07.013.005.00.001.000.000.000.000.000 3.000.014.071.15.1.58.57.5.177.16.081.046.03.010.004.001.000.000.000.000 4.000.001.016.054.111.17.0.43.36.06.161.113.070.038.017.006.00.000.000.000 5.000.000.00.013.039.080.13.183.1.36.6.193.147.099.057.07.010.00.000.000
Table 4 cotiued p r.01.05.10.15.0.5.30.35.40.45.50.55.60.65.70.75.80.85.90.95 11 6.000.000.000.00.010.07.057.099.147.193.6.36.1.183.13.080.039.013.00.000 7.000.000.000.000.00.006.017.038.070.113.161.06.36.43.0.17.111.054.016.001 8.000.000.000.000.000.001.004.010.03.046.081.16.177.5.57.58.1.15.071.014 9.000.000.000.000.000.000.001.00.005.013.07.051.089.140.00.58.95.87.13.087 10.000.000.000.000.000.000.000.000.001.00.005.013.07.05.093.155.36.35.384.39 11.000.000.000.000.000.000.000.000.000.000.000.001.004.009.00.04.086.167.314.569 1 0.886.540.8.14.069.03.014.006.00.001.000.000.000.000.000.000.000.000.000.000 1.107.341.377.301.06.17.071.037.017.008.003.001.000.000.000.000.000.000.000.000.006.099.30.9.83.3.168.109.064.034.016.007.00.001.000.000.000.000.000.000 3.000.017.085.17.36.58.40.195.14.09.054.08.01.005.001.000.000.000.000.000 4.000.00.01.068.133.194.31.37.13.170.11.076.04.00.008.00.001.000.000.000 5.000.000.004.019.053.103.158.04.7.3.193.149.101.059.09.011.003.001.000.000 6.000.000.000.004.016.040.079.18.177.1.6.1.177.18.079.040.016.004.000.000 7.000.000.000.001.003.011.09.059.101.149.193.3.7.04.158.103.053.019.004.000 8.000.000.000.000.001.00.008.00.04.076.11.170.13.37.31.194.133.068.01.00 9.000.000.000.000.000.000.001.005.01.08.054.09.14.195.40.58.36.17.085.017 10.000.000.000.000.000.000.000.001.00.007.016.034.064.109.168.3.83.9.30.099 11.000.000.000.000.000.000.000.000.000.001.003.008.017.037.071.17.06.301.377.341 1.000.000.000.000.000.000.000.000.000.000.000.001.00.006.014.03.069.14.8.540 15 0.860.463.06.087.035.013.005.00.000.000.000.000.000.000.000.000.000.000.000.000 1.130.366.343.31.13.067.031.013.005.00.000.000.000.000.000.000.000.000.000.000.009.135.67.86.31.156.09.048.0.009.003.001.000.000.000.000.000.000.000.000 3.000.031.19.18.50.5.170.111.063.03.014.005.00.000.000.000.000.000.000.000 4.000.005.043.116.188.5.19.179.17.078.04.019.007.00.001.000.000.000.000.000 5.000.001.010.045.103.165.06.1.186.140.09.051.04.010.003.001.000.000.000.000 6.000.000.00.013.043.09.147.191.07.191.153.105.061.030.01.003.001.000.000.000 7.000.000.000.003.014.039.081.13.177.01.196.165.118.071.035.013.003.001.000.000 8.000.000.000.001.003.013.035.071.118.165.196.01.177.13.081.039.014.003.000.000 9.000.000.000.000.001.003.01.030.061.105.153.191.07.191.147.09.043.013.00.000 10.000.000.000.000.000.001.003.010.04.051.09.140.186.1.06.165.103.045.010.001 11.000.000.000.000.000.000.001.00.007.019.04.078.17.179.19.5.188.116.043.005 1.000.000.000.000.000.000.000.000.00.005.014.03.063.111.170.5.50.18.19.031 13.000.000.000.000.000.000.000.000.000.001.003.009.0.048.09.156.31.86.67.135 14.000.000.000.000.000.000.000.000.000.000.000.00.005.013.031.067.13.31.343.366 15.000.000.000.000.000.000.000.000.000.000.000.000.000.00.005.013.035.087.06.463 16 0.851.440.185.074.08.010.003.001.000.000.000.000.000.000.000.000.000.000.000.000 1.138.371.39.10.113.053.03.009.003.001.000.000.000.000.000.000.000.000.000.000
Table 4 cotiued p r.01.05.10.15.0.5.30.35.40.45.50.55.60.65.70.75.80.85.90.95 16.010.146.75.77.11.134.073.035.015.006.00.001.000.000.000.000.000.000.000.000 3.000.036.14.9.46.08.146.089.047.0.009.003.001.000.000.000.000.000.000.000 4.000.006.051.131.00.5.04.155.101.057.08.011.004.001.000.000.000.000.000.000 5.000.001.014.056.10.180.10.01.16.11.067.034.014.005.001.000.000.000.000.000 6.000.000.003.018.055.110.165.198.198.168.1.075.039.017.006.001.000.000.000.000 7.000.000.000.005.00.05.101.15.189.197.175.13.084.044.019.006.001.000.000.000 8.000.000.000.001.006.00.049.09.14.181.196.181.14.09.049.00.006.001.000.000 9.000.000.000.000.001.006.019.044.084.13.175.197.189.15.101.05.00.005.000.000 10.000.000.000.000.000.001.006.017.039.075.1.168.198.198.165.110.055.018.003.000 11.000.000.000.000.000.000.001.005.014.034.067.11.16.01.10.180.10.056.014.001 1.000.000.000.000.000.000.000.001.004.011.08.057.101.155.04.5.00.131.051.006 13.000.000.000.000.000.000.000.000.001.003.009.0.047.089.146.08.46.9.14.036 14.000.000.000.000.000.000.000.000.000.001.00.006.015.035.073.134.11.77.75.146 15.000.000.000.000.000.000.000.000.000.000.000.001.003.009.03.053.113.10.39.371 16.000.000.000.000.000.000.000.000.000.000.000.000.000.001.003.010.08.074.185.440 0 0.818.358.1.039.01.003.001.000.000.000.000.000.000.000.000.000.000.000.000.000 1.165.377.70.137.058.01.007.00.000.000.000.000.000.000.000.000.000.000.000.000.016.189.85.9.137.067.08.010.003.001.000.000.000.000.000.000.000.000.000.000 3.001.060.190.43.05.134.07.03.01.004.001.000.000.000.000.000.000.000.000.000 4.000.013.090.18.18.190.130.074.035.014.005.001.000.000.000.000.000.000.000.000 5.000.00.03.103.175.0.179.17.075.036.015.005.001.000.000.000.000.000.000.000 6.000.000.009.045.109.169.19.171.14.075.037.015.005.001.000.000.000.000.000.000 7.000.000.00.016.055.11.164.184.166.1.074.037.015.005.001.000.000.000.000.000 8.000.000.000.005.0.061.114.161.180.16.10.073.035.014.004.001.000.000.000.000 9.000.000.000.001.007.07.065.116.160.177.160.119.071.034.01.003.000.000.000.000 10.000.000.000.000.00.010.031.069.117.159.176.159.117.069.031.010.00.000.000.000 11.000.000.000.000.000.003.01.034.071.119.160.177.160.116.065.07.007.001.000.000 1.000.000.000.000.000.001.004.014.035.073.10.16.180.161.114.061.0.005.000.000 13.000.000.000.000.000.000.001.005.015.037.074.1.166.184.164.11.055.016.00.000 14.000.000.000.000.000.000.000.001.005.015.037.075.14.171.19.169.109.045.009.000 15.000.000.000.000.000.000.000.000.001.005.015.036.075.17.179.0.175.103.03.00 16.000.000.000.000.000.000.000.000.000.001.005.014.035.074.130.190.18.18.090.013 17.000.000.000.000.000.000.000.000.000.000.001.004.01.03.07.134.05.43.190.060 18.000.000.000.000.000.000.000.000.000.000.000.001.003.010.08.067.137.9.85.189 19.000.000.000.000.000.000.000.000.000.000.000.000.000.00.007.01.058.137.70.377 0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.001.003.01.039.1.358
Table 5 Areas of a Stadard Normal Distributio The table etries represet the area uder the stadard ormal curve from 0 to the specified value of z. z.00.01.0.03.04.05.06.07.08.09 0.0 0.1 0. 0.3 0.4 0.5.0000.0398.0793.1179.1554.1915.0040.0438.083.117.1591.1950.0080.0478.0871.155.168.1985.010.0517.0910.193.1664.019.0160.0557.0948.1331.1700.054.0199.0596.0987.1368.1736.088.039.0636.106.1406.177.13.079.0675.1064.1443.1808.157.0319.0714.1103.1480.1844.190.0359.0753.1141.1517.1879.4 0.6 0.7 0.8 0.9 1.0.57.580.881.3159.3413.91.611.910.3186.3438.34.64.939.31.3461.357.673.967.338.3485.389.704.995.364.3508.4.734.303.389.3531.454.764.3051.3315.3554.486.794.3078.3340.3577.517.83.3106.3365.3599.549.85.3133.3389.361 1.1 1. 1.3 1.4 1.5.3643.3849.403.419.433.3665.3869.4049.407.4345.3686.3888.4066.4.4357.3708.3907.408.436.4370.379.395.4099.451.438.3749.3944.4115.465.4394.3770.396.4131.479.4406.3790.3980.4147.49.4418.3810.3997.416.4306.449.3830.4015.4177.4319.4441 1.6 1.7 1.8 1.9.0.445.4554.4641.4713.477.4463.4564.4649.4719.4778.4474.4573.4656.476.4783.4484.458.4664.473.4788.4495.4591.4671.4738.4793.4505.4599.4678.4744.4798.4515.4608.4686.4750.4803.455.4616.4693.4756.4808.4535.465.4699.4761.481.4545.4633.4706.4767.4817.1..3.4.5 :481.4861.4893.4918.4938.486.4864.4896.490.4940 :4830.4868.4898.49.4941.4834.4871.4901.495.4943.4838.4875.4904.497.4945.484.4878.4906.499.4946.4846.4881.4909.4931.4948.4850.4884.4911.493.4949.4854.4887.4913.4934.4951.4857.4890.4916.4936.495.6.7.8.9 3.0.4953.4965.4974.4981.4987.4955.4966.4975.498.4987.4956.4967.4976.498.4987.4957.4968.4977.4983.4988.4959.4969.4977.4984.4988.4960.4970.4978.4984.4989.4961.4971.4979.4985.4989.496.497.4979.4985.4989.4963.4973.4980.4986.4990.4964.4974.4981.4986.4990 3.1 3. 3.3 3.4 3.5 3.6.4990.4993.4991.4993.4991.4994.4991.4994.499.4994.499.4994.499.4994.499.4993.4993 For values of z greater tha or equal to 3.70, use 0 to approximate the shaded area uder the stadard ormal curve.
Table 6 Studet s t Distributio Studet s t values geerated by Miitab Versio 9. c 0.750 0.800 0.850 0.900 0.950 0.980 0.990 a 0.15 0.100 0.075 0.050 0.05 0.010 0.005 a 0.50 0.00 0.150 0.100 0.050 0.00 0.010 d.f. 1.414 3.078 4.165 6.314 1.706 31.81 63.657 1.604 1.886.8.90 4.303 6.965 9.95 c is a cofidece level: 3 1.43 1.638 1.94.353 3.18 4.541 5.841 4 1.344 1.533 1.778.13.776 3.747 4.604 5 1.301 1.476 1.699.015.571 3.365 4.03 6 1.73 1.440 1.650 1.943.447 3.143 3.707 7 1.54 1.415 1.617 1.895.365.998 3.499 8 1.40 1.397 1.59 1.860.306.896 3.355 9 1.30 1.383 1.574 1.833.6.81 3.50 10 1.1 1.37 1.559 1.81.8.764 3.169 11 1.14 1.363 1.548 1.796.01.718 3.106 1 1.09 1.356 1.538 1.78.179.681 3.055 a is the level of sigificace for a oe-tailed test: 13 1.04 1.350 1.530 1.771.160.650 3.01 14 1.00 1.345 1.53 1.761.145.64.977 15 1.197 1.341 1.517 1.753.131.60.947 16 1.194 1.337 1.51 1.746.10.583.91 17 1.191 1.333 1.508 1.740.110.567.898 18 1.189 1.330 1.504 1.734.101.55.878 19 1.187 1.38 1.500 1.79.093.539.861 0 1.185 1.35 1.497 1.75.086.58.845 1 1.183 1.33 1.494 1.71.080.518.831 1.18 1.31 1.49 1.717.074.508.819 3 1.180 1.319 1.489 1.714.069.500.807 4 1.179 1.318 1.487 1.711.064.49.797 5 1.178 1.316 1.485 1.708.060.485.787 6 1.177 1.315 1.483 1.706.056.479.779 7 1.176 1.314 1.48 1.703.05.473.771 8 1.175 1.313 1.480 1.701.048.467.763 9 1.174 1.311 1.479 1.699.045.46.756 a is the level of sigificace for a two-tailed test 30 1.173 1.310 1.477 1.697.04.457.750 35 1.170 1.306 1.47 1.690.030.438.74 40 1.167 1.303 1.468 1.684.01.43.704 45 1.165 1.301 1.465 1.679.014.41.690 50 1.164 1.99 1.46 1.676.009.403.678 55 1.163 1.97 1.460 1.673.004.396.668 60 1.16 1.96 1.458 1.671.000.390.660 90 1.158 1.91 1.45 1.66 1.987.369.63 10 1.156 1.89 1.449 1.658 1.980.358.617 cc 1.15 1.8 1.44 1.645 1.96.33.58
Areas of a Stadard Normal Distributio The table etries represet the area uder the stadard ormal curve from 0 to the specified value of z. z.00.01.0.03.04.05.06.07.08.09 0.0 0.1 0. 0.3 0.4 0.5.0000.0398.0793.1179.1554.1915.0040.0438.083.117.1591.1950.0080.0478.0871.155.168.1985.010.0517.0910.193.1664.019.0160.0557.0948.1331.1700.054.0199.0596.0987.1368.1736.088.039.0636.106.1406.177.13.079.0675.1064.1443.1808.157.0319.0714.1103.1480.1844.190.0359.0753.1141.1517.1879.4 0.6.57.91.34.357.389.4.454.486.517.549 0.7.580.611.64.673.704.734.764.794.83.85 0.8.881.910.939.967.995.303.3051.3078.3106.3133 0.9.3159.3186.31.338.364.389.3315.3340.3365.3389 1.0.3413.3438.3461.3485.3508.3531.3554.3577.3599.361 1.1.3643.3665.3686.3708.379.3749.3770.3790.3810.3830 1..3849.3869.3888.3907.395.3944.396.3980.3997.4015 1.3.403.4049.4066.408.4099.4115.4131.4147.416.4177 1.4.419.407.4.436.451.465.479.49.4306.4319 1.5.433.4345.4357.4370.438.4394.4406.4418.449.4441 1.6.445.4463.4474.4484.4495.4505.4515.455.4535.4545 1.7.4554.4564.4573.458.4591.4599.4608.4616.465.4633 1.8.4641.4649.4656.4664.4671.4678.4686.4693.4699.4706 1.9.4713.4719.476.473.4738.4744.4750.4756.4761.4767.0.477.4778.4783.4788.4793.4798.4803.4808.481.4817.1 :481.486 :4830.4834.4838.484.4846.4850.4854.4857..4861.4864.4868.4871.4875.4878.4881.4884.4887.4890.3.4893.4896.4898.4901.4904.4906.4909.4911.4913.4916.4.4918.490.49.495.497.499.4931.493.4934.4936.5.4938.4940.4941.4943.4945.4946.4948.4949.4951.495.6.4953.4955.4956.4957.4959.4960.4961.496.4963.4964.7.4965.4966.4967.4968.4969.4970.4971.497.4973.4974.8.4974.4975.4976.4977.4977.4978.4979.4979.4980.4981.9.4981.498.498.4983.4984.4984.4985.4985.4986.4986 3.0.4987.4987.4987.4988.4988.4989.4989.4989.4990.4990 3.1.4990.4991.4991.4991.499.499.499.499.4993.4993 3..4993.4993.4994.4994.4994.4994.4994 3.3 3.4 3.5 3.6 For values of z greater tha or equal to 3.70, use 0 to approximate the shaded area uder the stadard ormal curve.
Some Levels of Cofidece ad Their Correspodig Critical Values Commoly Used Critical Values z 0 from the Stadard Normal Distributio Level of Cofidece c Critical Value z c Type of Test Level of Sigificace 0.75 1.15 0.05 0.01 0.80 1.8 0.85 1.44 Left-tailed - 1.645 -.33 0.90 1.645 Right-tailed 1.645.33 0.95 1.96 Two-tailed ±1.96 ±.58 0.99.58 Table 8 Critical Values of Pearso Product-Momet Correlatio Coefficiet, r a =0.01 a = 0.05 oe tail two tails oe tail two tails 3 1.00 1.00.99 1.00 For a right-tailed test, use a positive r value: 4.98.99.90.95 5.93.96.81.88 6.88.9.73.81 7.83.87.67.75 8.79.83.6.71 9.75.80.58.67 10.7.76.54.63 11.69.73.5.60 1.66.71.50.58 For a left-tailed test, use a egative r value: 13.63.68.48.53 14.61.66.46.53 15.59.64.44.51 16.57.6.4.50 17.56.61.41.48 18.54.59.40.47 19.53.58.39.46 0.5.56.38.44 1.50.55.37.43.49.54.36.4 For a two-tailed test, use a positive r value 3.48.53.35.41 ad egative r value: 4.47.5.34.40 5.46.51.34.40 6.45.50.33.39 7.45.49.3.38 8.44.48.3.37 9.43.47.31.37 30.4.46.31.36
Frequetly Used Formulas = sample size N = populatio size f = frequecy Chapter 1 high low Class Width = (icrease to ext umber of classes iteger) upperlimit + lowerlimit Class Midpoit = Lower boudary = lower boudary of previous class + class width Chapter Sample mea X = x x Populatio mea µ = N Rage = largest data value - smallest data value Sample stadard deviatios s = Computatio formula s = SS x = x ( x) SS x 1 Populatio stadard deviatio σ = Sample variace s Populatio variace o (x x) 1 where ( x µ ) s Sample Coefficiet of Variatio CV = 100 x Sample mea for grouped data x = xf Sample stadard deviatio for grouped data s = Chapter 3 ( x x) f 1 Regressio ad Correlatio I all these formulas ( x) SS x = x ( y ) SS y = y SS xy = xy ( x)( y ) N Least squares lie y = a + bx where b = SS xy ad SS x a = y bx Pearso product-momet correlatio coefficiet r = SS xy SS x SS y Coefficiet of determiatio Chapter 4 = r Probability of the complemet of evet A P ot A = 1 P A ( ) ( ) Multiplicatio rule for idepedet evets P A ad B = P A P B ( ) ( ) ( ) Geeral multiplicatio rules P A ad B = P A P B, give ( ) ( ) ( A) ( A ad B) = P( B) P( A give B) P, Additio rule for mutually exclusive evets P A or B = P A + P B ( ) ( ) ( ) Geeral additio rule P A or B = P A + P B ( ) ( ) ( ) P( A ad B) Permutatio rule P,r! = ( r )!! Combiatio rule C,r = r! ( r )! Chapter 5 Mea of a discrete probability distributio µ = xp( x) Stadard deviatio of a discrete probability distributio ( x µ ) P( ) σ = x For Biomial Distributios r = umber of successes; p = probability of success; q = 1 p Biomial probability distributio P(r) = r! ( Mea µ = p Stadard deviatio Chapter 6 σ = Raw score x = zσ + µ x µ Stadard score z = σ pq! r r p q r)!
Chapter 7 Mea of x distributio µ x = µ Stadard deviatio of x distributio σ x = Stadard score for x Chapter 8 Cofidece Iterval µ whe 30 for ( ) x z σ < µ < x c + for µ ( whe < 30) d.f. = 1 s x t c < µ < x + t z c x µ z = σ for p ( whe p > 5 ad q > 5) pˆ ( 1 pˆ ) pˆ ( 1 pˆ ) c s σ pˆ zc < p < pˆ + zc where pˆ = r/ Sample Size for Estimatig zc σ meas = E proportios zc = p( 1 p) with prelimiary estimate for p E 1 zc = without prelimiary estimate for p 4 E Chapter 9 Sample Test Statistics for Tests of Hypotheses for µ ( whe 30) for ( whe 30) x µ z = σ x µ µ < ; t = with d.f. = 1 pˆ p for p z = where q = 1 p pq Chapter 10 Sample Test Statistics for Tests of Hypothesis for paired differece d t = d µ d with d.f. = 1 s sd differece of meas large sample ( x1 x ) ( µ µ ) 1 z = σ1 σ = 1 σ differece of proportios pˆ 1 pˆ r 1 + r z = where pˆ = ; qˆ = 1 pˆ ; pˆ qˆ pˆ qˆ 1 + + 1 pˆ = r 1 1; pˆ r = 1 Cofidece Itervals for differece of meas (whe 1 30 ad 30 ) σ σ x x z 1 x x 1 ( 1 ) + < µ µ < ( 1 ) σ 1 σ + z + 1 for differece of proportios where pˆ = r 1 pˆ = r qˆ = 1 pˆ ; qˆ = pˆ ; 1 1 1 1 pˆ qˆ pˆ qˆ pˆ z 1 1 1 1 1 1 ( pˆ ) + < pˆ pˆ < ( pˆ pˆ ) + zc pˆ qˆ 1 1 + 1 Chapter 11 ( O E) x = where E row total colum E = sample size pˆ qˆ ( )( total ) Tests of idepedece d. f. = ( R 1)( C 1) Goodess of fit d. f. = ( umber of etries) 1 Sample test statistic for H 0 : σ = k; d.f. = 1 ( 1) s x = σ Liear Regressio Stadard error or estimate Se = SSxy where b = SSy Cofidece iterval for y y SS y bss E < y E where y p is the predicted y value p p + for x ad ( x x ) 1 E = t c Se 1+ + with d. f. = SS x xy