AtlasMasuk

Lembar persamaan

Rumus dan tabel AP Statistics, baris demi baris. Setiap rumus ditautkan ke semua halaman atlas yang menampilkan atau memakainya.

AP Statistics

Rumus · diberikan pada ujian

I. Statistika deskriptif

nn = ukuran sampel · xˉ,yˉ\bar{x}, \bar{y} = rata-rata sampel · sx,sys_x, s_y = simpangan baku sampel · rr = korelasi · y^\hat{y} = respons prediksi · aa = intersep-y · bb = kemiringan

II. Peluang dan distribusi

A,BA, B = kejadian · XX = variabel acak · nn = banyak percobaan · pp = peluang sukses pada setiap percobaan

  • P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)
  • P(A∣B)=P(A∩B)P(B)\displaystyle P(A \mid B) = \frac{P(A \cap B)}{P(B)}
  • μX=E(X)=∑xiP(xi)σX=∑(xi−μX)2P(xi)\mu_X = E(X) = \sum x_iP(x_i) \qquad \sigma_X = \sqrt{\sum(x_i - \mu_X)^2P(x_i)}
    Variabel acak diskret: rata-rata dan simpangan baku4.8 Rata-rata dan simpangan baku variabel acak
  • P(X=x)=(nx)px(1−p)n−x, x=0,1,…,nμX=npσX=np(1−p)P(X = x) = \binom{n}{x}p^x(1-p)^{n-x},\ x = 0, 1, \dots, n \qquad \mu_X = np \qquad \sigma_X = \sqrt{np(1-p)}
  • P(X=x)=(1−p)x−1p, x=1,2,3,…μX=1pσX=1−pp\displaystyle P(X = x) = (1-p)^{x-1}p,\ x = 1, 2, 3, \dots \qquad \mu_X = \frac{1}{p} \qquad \sigma_X = \frac{\sqrt{1-p}}{p}
    Distribusi geometrik4.12 Distribusi geometrik

III. Distribusi sampling dan statistika inferensial

Bentuk umum, untuk setiap prosedur di bawah ini.

Distribusi sampling untuk proporsi

pp = proporsi populasi · p^\hat{p} = proporsi sampel · p^c\hat{p}_c = (X_1 + X_2)/(n_1 + n_2), proporsi gabungan (pooled) · σ\sigma = simpangan baku statistik · ss = galat bakunya

  • μp^=pσp^=p(1−p)nsp^=p^(1−p^)n\displaystyle \mu_{\hat{p}} = p \qquad \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} \qquad s_{\hat{p}} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
  • μp^1−p^2=p1−p2σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2\displaystyle \mu_{\hat{p}_1-\hat{p}_2} = p_1 - p_2 \qquad \sigma_{\hat{p}_1-\hat{p}_2} = \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}
  • sp^1−p^2=p^1(1−p^1)n1+p^2(1−p^2)n2\displaystyle s_{\hat{p}_1-\hat{p}_2} = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}
    Galat bakunya (interval)6.8 Interval untuk selisih
  • sp^1−p^2=p^c(1−p^c)(1n1+1n2)\displaystyle s_{\hat{p}_1-\hat{p}_2} = \sqrt{\hat{p}_c(1-\hat{p}_c)\Big(\frac{1}{n_1} + \frac{1}{n_2}\Big)}
    Galat bakunya bila diasumsikan p₁ = p₂ (uji)6.10 Menyusun uji dua sampel6.11 Melakukan uji dua sampel

Distribusi sampling untuk rata-rata

μ\mu = rata-rata populasi · σ\sigma = simpangan baku populasi · xˉ\bar{x} = rata-rata sampel · ss = simpangan baku sampel

Distribusi sampling untuk regresi linear sederhana

β\beta = kemiringan populasi · bb = kemiringan sampel · σ\sigma = simpangan baku y terhadap garis · ss = simpangan baku residual · sxs_x = simpangan baku x

Tabel

Normal, t, dan khi-kuadrat · diberikan pada ujian

Tabel A: peluang normal baku, peluang di bawah z

z.00.01.02.03.04.05.06.07.08.09
−3.4.0003.0003.0003.0003.0003.0003.0003.0003.0003.0002
−3.3.0005.0005.0005.0004.0004.0004.0004.0004.0004.0003
−3.2.0007.0007.0006.0006.0006.0006.0006.0005.0005.0005
−3.1.0010.0009.0009.0009.0008.0008.0008.0008.0007.0007
−3.0.0013.0013.0013.0012.0012.0011.0011.0011.0010.0010
−2.9.0019.0018.0018.0017.0016.0016.0015.0015.0014.0014
−2.8.0026.0025.0024.0023.0023.0022.0021.0021.0020.0019
−2.7.0035.0034.0033.0032.0031.0030.0029.0028.0027.0026
−2.6.0047.0045.0044.0043.0041.0040.0039.0038.0037.0036
−2.5.0062.0060.0059.0057.0055.0054.0052.0051.0049.0048
−2.4.0082.0080.0078.0075.0073.0071.0069.0068.0066.0064
−2.3.0107.0104.0102.0099.0096.0094.0091.0089.0087.0084
−2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110
−2.1.0179.0174.0170.0166.0162.0158.0154.0150.0146.0143
−2.0.0228.0222.0217.0212.0207.0202.0197.0192.0188.0183
−1.9.0287.0281.0274.0268.0262.0256.0250.0244.0239.0233
−1.8.0359.0351.0344.0336.0329.0322.0314.0307.0301.0294
−1.7.0446.0436.0427.0418.0409.0401.0392.0384.0375.0367
−1.6.0548.0537.0526.0516.0505.0495.0485.0475.0465.0455
−1.5.0668.0655.0643.0630.0618.0606.0594.0582.0571.0559
−1.4.0808.0793.0778.0764.0749.0735.0721.0708.0694.0681
−1.3.0968.0951.0934.0918.0901.0885.0869.0853.0838.0823
−1.2.1151.1131.1112.1093.1075.1056.1038.1020.1003.0985
−1.1.1357.1335.1314.1292.1271.1251.1230.1210.1190.1170
−1.0.1587.1562.1539.1515.1492.1469.1446.1423.1401.1379
−0.9.1841.1814.1788.1762.1736.1711.1685.1660.1635.1611
−0.8.2119.2090.2061.2033.2005.1977.1949.1922.1894.1867
−0.7.2420.2389.2358.2327.2296.2266.2236.2206.2177.2148
−0.6.2743.2709.2676.2643.2611.2578.2546.2514.2483.2451
−0.5.3085.3050.3015.2981.2946.2912.2877.2843.2810.2776
−0.4.3446.3409.3372.3336.3300.3264.3228.3192.3156.3121
−0.3.3821.3783.3745.3707.3669.3632.3594.3557.3520.3483
−0.2.4207.4168.4129.4090.4052.4013.3974.3936.3897.3859
−0.1.4602.4562.4522.4483.4443.4404.4364.4325.4286.4247
−0.0.5000.4960.4920.4880.4840.4801.4761.4721.4681.4641
0.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.5359
0.1.5398.5438.5478.5517.5557.5596.5636.5675.5714.5753
0.2.5793.5832.5871.5910.5948.5987.6026.6064.6103.6141
0.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.6517
0.4.6554.6591.6628.6664.6700.6736.6772.6808.6844.6879
0.5.6915.6950.6985.7019.7054.7088.7123.7157.7190.7224
0.6.7257.7291.7324.7357.7389.7422.7454.7486.7517.7549
0.7.7580.7611.7642.7673.7704.7734.7764.7794.7823.7852
0.8.7881.7910.7939.7967.7995.8023.8051.8078.8106.8133
0.9.8159.8186.8212.8238.8264.8289.8315.8340.8365.8389
1.0.8413.8438.8461.8485.8508.8531.8554.8577.8599.8621
1.1.8643.8665.8686.8708.8729.8749.8770.8790.8810.8830
1.2.8849.8869.8888.8907.8925.8944.8962.8980.8997.9015
1.3.9032.9049.9066.9082.9099.9115.9131.9147.9162.9177
1.4.9192.9207.9222.9236.9251.9265.9279.9292.9306.9319
1.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.9441
1.6.9452.9463.9474.9484.9495.9505.9515.9525.9535.9545
1.7.9554.9564.9573.9582.9591.9599.9608.9616.9625.9633
1.8.9641.9649.9656.9664.9671.9678.9686.9693.9699.9706
1.9.9713.9719.9726.9732.9738.9744.9750.9756.9761.9767
2.0.9772.9778.9783.9788.9793.9798.9803.9808.9812.9817
2.1.9821.9826.9830.9834.9838.9842.9846.9850.9854.9857
2.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.9890
2.3.9893.9896.9898.9901.9904.9906.9909.9911.9913.9916
2.4.9918.9920.9922.9925.9927.9929.9931.9932.9934.9936
2.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.9952
2.6.9953.9955.9956.9957.9959.9960.9961.9962.9963.9964
2.7.9965.9966.9967.9968.9969.9970.9971.9972.9973.9974
2.8.9974.9975.9976.9977.9977.9978.9979.9979.9980.9981
2.9.9981.9982.9982.9983.9984.9984.9985.9985.9986.9986
3.0.9987.9987.9987.9988.9988.9989.9989.9989.9990.9990
3.1.9990.9991.9991.9991.9992.9992.9992.9992.9993.9993
3.2.9993.9993.9994.9994.9994.9994.9994.9995.9995.9995
3.3.9995.9995.9995.9996.9996.9996.9996.9996.9996.9997
3.4.9997.9997.9997.9997.9997.9997.9997.9997.9997.9998

Tabel B: nilai kritis distribusi t, titik t* dengan peluang p di atasnya dan C di antara −t* dan t*

df0.250.20.150.10.050.0250.020.010.0050.00250.0010.0005
11.0001.3761.9633.0786.31412.7115.8931.8263.66127.3318.3636.6
2.8161.0611.3861.8862.9204.3034.8496.9659.92514.0922.3331.60
3.765.9781.2501.6382.3533.1823.4824.5415.8417.45310.2112.92
4.741.9411.1901.5332.1322.7762.9993.7474.6045.5987.1738.610
5.727.9201.1561.4762.0152.5712.7573.3654.0324.7735.8936.869
6.718.9061.1341.4401.9432.4472.6123.1433.7074.3175.2085.959
7.711.8961.1191.4151.8952.3652.5172.9983.4994.0294.7855.408
8.706.8891.1081.3971.8602.3062.4492.8963.3553.8334.5015.041
9.703.8831.1001.3831.8332.2622.3982.8213.2503.6904.2974.781
10.700.8791.0931.3721.8122.2282.3592.7643.1693.5814.1444.587
11.697.8761.0881.3631.7962.2012.3282.7183.1063.4974.0254.437
12.695.8731.0831.3561.7822.1792.3032.6813.0553.4283.9304.318
13.694.8701.0791.3501.7712.1602.2822.6503.0123.3723.8524.221
14.692.8681.0761.3451.7612.1452.2642.6242.9773.3263.7874.140
15.691.8661.0741.3411.7532.1312.2492.6022.9473.2863.7334.073
16.690.8651.0711.3371.7462.1202.2352.5832.9213.2523.6864.015
17.689.8631.0691.3331.7402.1102.2242.5672.8983.2223.6463.965
18.688.8621.0671.3301.7342.1012.2142.5522.8783.1973.6113.922
19.688.8611.0661.3281.7292.0932.2052.5392.8613.1743.5793.883
20.687.8601.0641.3251.7252.0862.1972.5282.8453.1533.5523.850
21.686.8591.0631.3231.7212.0802.1892.5182.8313.1353.5273.819
22.686.8581.0611.3211.7172.0742.1832.5082.8193.1193.5053.792
23.685.8581.0601.3191.7142.0692.1772.5002.8073.1043.4853.768
24.685.8571.0591.3181.7112.0642.1722.4922.7973.0913.4673.745
25.684.8561.0581.3161.7082.0602.1672.4852.7873.0783.4503.725
26.684.8561.0581.3151.7062.0562.1622.4792.7793.0673.4353.707
27.684.8551.0571.3141.7032.0522.1582.4732.7713.0573.4213.690
28.683.8551.0561.3131.7012.0482.1542.4672.7633.0473.4083.674
29.683.8541.0551.3111.6992.0452.1502.4622.7563.0383.3963.659
30.683.8541.0551.3101.6972.0422.1472.4572.7503.0303.3853.646
40.681.8511.0501.3031.6842.0212.1232.4232.7042.9713.3073.551
50.679.8491.0471.2991.6762.0092.1092.4032.6782.9373.2613.496
60.679.8481.0451.2961.6712.0002.0992.3902.6602.9153.2323.460
80.678.8461.0431.2921.6641.9902.0882.3742.6392.8873.1953.416
100.677.8451.0421.2901.6601.9842.0812.3642.6262.8713.1743.390
1000.675.8421.0371.2821.6461.9622.0562.3302.5812.8133.0983.300
∞.674.8411.0361.2821.6451.9602.0542.3262.5762.8073.0913.291
C50%60%70%80%90%95%96%98%99%99.5%99.8%99.9%

Tabel C: nilai kritis χ², titik dengan peluang p di atasnya

df0.250.20.150.10.050.0250.020.010.0050.00250.0010.0005
11.321.642.072.713.845.025.416.637.889.1410.8312.12
22.773.223.794.615.997.387.829.2110.6011.9813.8215.20
34.114.645.326.257.819.359.8411.3412.8414.3216.2717.73
45.395.996.747.789.4911.1411.6713.2814.8616.4218.4720.00
56.637.298.129.2411.0712.8313.3915.0916.7518.3920.5122.11
67.848.569.4510.6412.5914.4515.0316.8118.5520.2522.4624.10
79.049.8010.7512.0214.0716.0116.6218.4820.2822.0424.3226.02
810.2211.0312.0313.3615.5117.5318.1720.0921.9523.7726.1227.87
911.3912.2413.2914.6816.9219.0219.6821.6723.5925.4627.8829.67
1012.5513.4414.5315.9918.3120.4821.1623.2125.1927.1129.5931.42
1113.7014.6315.7717.2819.6821.9222.6224.7226.7628.7331.2633.14
1214.8515.8116.9918.5521.0323.3424.0526.2228.3030.3232.9134.82
1315.9816.9818.2019.8122.3624.7425.4727.6929.8231.8834.5336.48
1417.1218.1519.4121.0623.6826.1226.8729.1431.3233.4336.1238.11
1518.2519.3120.6022.3125.0027.4928.2630.5832.8034.9537.7039.72
1619.3720.4721.7923.5426.3028.8529.6332.0034.2736.4639.2541.31
1720.4921.6122.9824.7727.5930.1931.0033.4135.7237.9540.7942.88
1821.6022.7624.1625.9928.8731.5332.3534.8137.1639.4242.3144.43
1922.7223.9025.3327.2030.1432.8533.6936.1938.5840.8843.8245.97
2023.8325.0426.5028.4131.4134.1735.0237.5740.0042.3445.3147.50
2124.9326.1727.6629.6232.6735.4836.3438.9341.4043.7846.8049.01
2226.0427.3028.8230.8133.9236.7837.6640.2942.8045.2048.2750.51
2327.1428.4329.9832.0135.1738.0838.9741.6444.1846.6249.7352.00
2428.2429.5531.1333.2036.4239.3640.2742.9845.5648.0351.1853.48
2529.3430.6832.2834.3837.6540.6541.5744.3146.9349.4452.6254.95
2630.4331.7933.4335.5638.8941.9242.8645.6448.2950.8354.0556.41
2731.5332.9134.5736.7440.1143.1944.1446.9649.6452.2255.4857.86
2832.6234.0335.7137.9241.3444.4645.4248.2850.9953.5956.8959.30
2933.7135.1436.8539.0942.5645.7246.6949.5952.3454.9758.3060.73
3034.8036.2537.9940.2643.7746.9847.9650.8953.6756.3359.7062.16
4045.6247.2749.2451.8155.7659.3460.4463.6966.7769.7073.4076.09
5056.3358.1660.3563.1767.5071.4272.6176.1579.4982.6686.6689.56
6066.9868.9771.3474.4079.0883.3084.5888.3891.9595.3499.61102.7
8088.1390.4193.1196.58101.9106.6108.1112.3116.3120.1124.8128.3
100109.1111.7114.7118.5124.3129.6131.1135.8140.2144.3149.4153.2

Tidak ada persamaan yang cocok.