T-Test Hypothesis in Stats

T-Test Hypothesis in Stats

t-test exercises

Use the wcgs_ex data file for these exercises.

  1. Test the hypothesis that those without CHD smoke less than 10 cigarettes per day.
  2. Test the hypothesis that smokers are older than non-smokers
  3. Test the hypothesis that those with CHD have a higher systolic blood pressure than those without CHD
  4. Test the hypothesis that those with CHD smoke more than those without CHD
  5. Test the hypothesis that a treatment is effective in lowering BMI.
  6. Test the hypothesis that a treatment is effective in lowering cholesterol. 

Solution 

Difference in chol_treatment Difference in chol_ notreatment
9.5532042 -5.22116
8.0236278 -5.564
0.9638601 -9.64553
2.1049392 -1.52062
1.0768146 -4.01406
-6.1339976 -4.01754
-2.0469639 1.722191
6.7689261 1.723862
3.5101325 5.750359
-3.637515 1.562886
0.0929467 -2.61522
-0.1491049 -1.67489
-8.7686737 -2.29243
0.9583132 4.961956
-0.1048182 5.517935
-7.6114216 0.137521
0.7036518 -1.72983
0.1182464 -6.24221
5.2064978 5.366817
-6.6065195 0.506763
-11.9597654 -6.88299
-2.2379634 -4.15774
0.5296153 -8.38814
15.3110304 -2.59792
3.1709938 5.292156
7.3741941 -3.13191
-9.5188054 -2.24094
-2.6439492 1.40852
-4.7396888 -5.05095
-7.7800847 6.105121
2.0657844 1.286324
7.5599303 -6.2469
4.8718001 -3.0285
1.9099798 -2.9304
-8.0136371 -3.71414
5.5377478 0.663117
-2.0446072 2.310384
2.6916267 -3.92044
2.4683901 -1.18095
-2.4590926 2.306402
-19.4823626 -3.52584
3.1816622 -8.56531
-7.3093528 -1.77709
8.5279542 -1.4668
0.2117655 5.845501
-1.5765035 1.568646
-6.1935042 -6.6088
-2.7996912 4.964587
-0.8768718 3.563532
-6.5656582 12.37273
-2.3622614 5.737302
-4.0981015 1.645631
1.483601 0.959292
-6.2745487 -3.30573
-0.1012181 -1.85403
-5.8365389 -5.4638
-1.5215873 3.873142
-4.9532515 0.466384
1.4330986 -7.11502
2.4089798 -3.61051
-6.8539711 1.696331
3.9429428 -8.10272
2.3440281 0.263028
-6.224594 -0.81014
-7.0426909 4.569419
3.5339846 -1.09422
-2.43841
3.4625877 -4.29481
-9.4150805 -8.3285
-2.2680867 -2.2794
-4.1003678 -8.40816
-1.5825827 -8.68184
2.1280853 -4.09253
-0.6139906 6.734198
-1.8699363 2.940078
1.7192491 -8.65063
-2.4796142 5.697344
2.0969802 -4.29093
-7.7215911 -7.70353
-6.7100378 -10.9147
0.8508474 -3.44106
-3.1115773 -0.29101
7.4822055 3.327545
-0.5399642 -2.15372
-9.7908386 -2.46358
-17.2146684 -1.97134
7.8398748 -12.8782
-0.7925911 8.376374
-5.3528597 -5.38497
-0.3555023 3.179841
-2.6698759 1.568565
-8.9149496 3.622612
-9.2323062 2.29125
2.6152139 -8.33064
-3.3647296 -1.29858
-2.598463 -5.87021
12.6356877 3.439447
-1.0156351 5.074896
-9.2845973 -3.60424
3.8716073 -4.63806
-10.0664365 -16.0038
5.3515291 -6.66378
-9.580009 -2.24521
0.4772774 -0.17247
-5.9801863 4.574953
2.0636933 0.393344
-4.1214888 -3.57235
-5.9494545 -0.28703
0.0816925 0.87882
0.1686765 -6.01705
7.3261107 1.518452
2.4569915 -6.01881
1.6692535 3.941457
-6.1774156 -3.94441
-1.7133002 -2.97401
-2.7710255 -1.3581
-5.7810854 -6.84353
5.5633498 -1.37656
-7.4871666 -10.326
-3.466267 4.28783
3.1150963 -4.6678
-7.6279095 -0.86935
7.2936709 -10.6891
-0.2612369 4.934789
-1.5108362 7.42475
0.7609176 6.134669
-0.7545083 -3.79699
8.571177 -1.44772
-3.8469047 -1.09804
-3.0153378 -8.20577
2.4792864 -5.40092
10.3097408 4.411424
1.4309145 8.176104
3.5754158 -1.90542
6.3898536 -3.79123
-1.6618227 -10.2705
-3.1712819 -7.98598
5.6570947 -11.7371
-3.8259719 -10.3866
-1.9051254 0.096574
-1.7015431 -5.54619
-5.9994748 -2.57972
-2.6383766 -4.44625
-2.4056831 1.971982
1.4972063 8.165773
5.9768789 -2.9682
2.5170163 -0.22497
-1.672099 4.11481
-5.7446929 -4.5455
-2.056624 0.743815
0.5539735 -6.60277
1.0657983 0.792013
-1.508295 -11.637
-7.7991733 1.969267
1.1829432 -7.30651
-2.7149235 0.426129
-3.0571382 -6.61314
2.0241066 2.772898
-0.3159165 0.796547
-7.7100126 0.115423
0.7096212 0.02372
-4.060784 6.598095
3.135433 5.210882
-8.1466279 -9.73649
0.4168165 3.490938
-5.8384028 0.477382
-1.1459588 -2.28692
-1.7010142 -0.22119
-4.0127519 -4.68661
5.3575215 -5.96882
-11.1653272 -0.52017
0.2414817 -7.62254
11.0859327 2.999974
-5.5201877 2.422894
12.317139 -1.59741
-1.3577376 0.209191
1.4241634 -4.76988
-1.4259955 -2.80486
4.8083553 8.56087
2.9491424 -1.57662
3.8433831 -0.3128
0.5107773 -2.75799
6.7126883 -5.08828
1.2270832 -2.02948
-8.9897676 -1.5537
6.1979374 -15.3354
3.8454282 -1.78628
-11.3084386 -0.52531
-11.7262469 -9.76527
-1.0001433 -4.98318
-1.8665116 1.902554
-2.0421611 -4.62333
3.3853994 1.631004
0.22863 0.055563
-2.5151837 -4.90641
0.0191924 -3.36578
-0.7907256 5.343304
-4.8652633 1.511449
5.3978402 2.689982
5.8513186 6.19867
-0.3857427 1.753959
-5.7076495 -0.60633
2.9259858 -4.37443
-3.6124078 -7.67934
-7.7004012 1.064645
-2.6193941 5.861217
-8.2035981 -4.23544
-9.0746374 -3.02321
2.5786719 0.493465
1.3574295 -2.48556
-4.2274583 1.957829
2.3191904 -0.22263
-3.6518142 -3.74688
3.6229391 -3.4649
5.5477838 -0.826
0.6499032 -0.79802
-7.4534077 -4.69258
-12.9791679 5.920403
1.4154721 -4.08088
-10.0456309 -2.00351
1.484375 -3.33314
-9.5815763 -4.52456
-0.5926821 0.21245
-8.4983018 4.178898
-3.2947839 -3.79601
2.9086944 -0.44097
3.9710875 -0.51465
-0.5128164 -12.8347
6.0269232 -1.65964
3.8616231 10.8796
-2.0920731 4.620357
0.0308005 1.28659
2.5112535 10.6226
1.8155429 4.78085
-5.6690438 -7.19028
-2.3070017 -0.17138
1.3987404 1.092553
7.8305955 2.08666
2.7964522 -1.86648
2.1307624 -2.80092
1.4219638 0.788827
3.9855349 -2.33086
-2.1199765 3.202976
0.8317952 -7.63712
-0.0370703 -3.33737
6.8935238 0.122827
1.2065702 -2.95369
0.4991737 4.913459
-6.7423816 8.153182
-0.3176611 -5.02529
-1.9196508 5.50632
-1.1066136 -3.4307
-12.952365 -3.36859
-1.4502541 0.104238
0.6325733 -5.4261
0.8789487 1.019476
-3.9747533 -7.16252
-0.9648808 -7.5204
-12.7063756 -1.06006
-7.5726646 -0.72343
1.0433202 0.827709
-2.5549862 -4.88762
-1.5857271 -2.28601
8.320325 -3.22755
-9.6472584 4.803537
6.0274561 4.055701
1.8328491 -5.55854
2.4476297 -6.00069
-4.1007321 0.332737
-2.870377 2.295875
0.9633648 4.55242
-3.4104847 -8.59435
2.5542721 3.010671
-4.8587493 -7.09688
-9.6450541 -2.7989
2.0713897 3.453214
6.9488266 1.795972
-4.4952249 -5.87645
1.0292773 3.215757
-0.1522047 -0.03348
-3.8893013 -3.16375
3.4454253 -5.18465
-1.7480527 -2.54062
2.6715908 -0.63946
-1.5062928 2.099727
2.7729562 -0.29645
3.472488 2.417701
1.4893339 -1.34787
-5.7489337 -3.03993
6.1627942 4.503029
-3.8797816 -6.9952
-3.1724526 -6.80817
4.6836084 -3.89401
-8.9454982 -3.41395
0.1452211 -3.38468
1.8834684 0.105164
8.724422 -4.62967
0.0941491 -5.49142
1.2779503 0.575725
0.7486737 4.522708
-3.0657306 5.608617
1.5164194 1.513136
6.0941572 -3.53713
3.4182384 -8.54367
6.1350993 -3.05344
0.5817308 -0.97752
-7.6364409 -0.59448
-4.8880253 -1.14756
-6.6420314 7.536159
4.8397646 -2.48282
12.9997574 -6.15333
-1.88508 4.082049
-2.4518233 0.911174
-7.1377655 -9.98483
-8.4263374 -1.42864
2.8470133 2.050577
-2.5541538 -4.93935
-2.8034566 0.298628
0.421265 5.045011
4.7953251 -7.84143
-8.0880537 -1.61196
-3.7950914 -5.69217
1.5005138 -2.34493
-1.582266 -11.6586
-0.718503 -2.90591
6.0568648 0.391235
3.9873107 -7.93843
-6.9394104 10.35726
-3.8978443 3.113714
-10.3775798 -2.02063
7.4887251 -5.50409
-3.8570319 -3.43516
3.6030751 -4.90604
-9.3502254 -2.94469
0.3407752 0.698917
2.3800779 -10.0531
-3.93487
4.8609967 1.989542
-1.3658184 -2.10963
0.7900103 2.107406
2.6032703 -1.72809
2.7861975 8.0701
0.8518737 -2.06938
-0.5925605 1.086615
-5.5485042 7.184115
3.5570035 -0.11155
5.8488844 -3.83419
-2.4166175 -1.98938
-9.0673835 6.905155
-7.9563086 -11.3196
2.5135667 2.844861
-9.5319229 -5.36568
2.6502166 0.675571
-2.0101598 -7.9337
-0.9192454 -3.9759
5.9576791 0.803799
3.6279142 0.243223
-1.7084819 -5.55364
5.9095531 6.509868
-1.3102168 -5.8805
-1.3020144 -3.55043
-1.0076425 6.20584
-10.5560382 -0.71847
0.7684435 -4.10309
3.6701388 0.683007
2.4568601 -10.7333
-2.9674514 3.211751
0.6323449 -3.60477
-4.9967166 4.820809
3.4527593 9.87308
5.0011299 8.552807
-6.7135526 -3.07673
-6.3567135 -0.82812
-5.8401728 4.586605
10.2798375 -6.07542
-4.387748 -9.46906
-0.019341 -3.14903
10.5747773 4.677113
2.4280957 -2.1379
3.630454 3.58871
-1.383739 3.140546
-5.9852158 -3.50431
0.8829785 -5.64582
-8.8266776 -1.42911
-0.797357 4.368702
1.0953357 -8.29045
2.1430415 -11.2154
-1.2250861 -7.06754
2.0824774 7.710097
2.116006 0.167868
3.5653053 -6.42617
-2.3121764 -4.25181
6.4810801 3.178648
-5.9082071 3.721871
-10.4506098 -2.38119
3.1582039 -2.88859
-1.9112673 -12.1871
2.1435581 0.233243
0.3234309 -9.13417
-4.7777569 -2.72702
-8.1724236 6.965191
-6.0745271 -0.66931
-10.1331592 -0.19156
-5.3800821 -6.44184
0.5894007 -1.96881
2.9423474 2.405131
-7.0071971 4.739063
-3.449934 0.576037
-0.2880423 -4.99503
7.1553457 4.722143
-5.871524 -4.07424
2.537305 11.19418
-4.0793826 2.409671
7.1997884 6.961425
3.8186758 -7.18203
-3.4315894 -13.7267
-1.7168961 -2.03145
1.1265411 3.462025
-9.2112934 -3.96985
-1.7870325 -6.20054
-0.3275518 3.79156
-1.27466 9.043675
3.3014859 -3.61936
6.7094961 -4.35332
9.914716
4.7658801 1.454389
-16.7655507 -0.12365
-2.0370654 -5.47375
-3.1084459 0.833703
-7.6491614 -0.39325
-5.4787775 -10.8262
2.4107789 1.743247
-1.7469368 -2.89377
-5.6182651 1.026298
-3.5054669 -1.45206
-10.689832 -6.96128
-9.2226582 -5.49368
2.5131863 2.45178
6.8791041 -0.5633
1.3328407 0.523723
0.3003609 -9.77868
0.0248961 -1.63737
-7.4846376 3.679145
2.7145546 0.01485
4.5842635 0.957516
-1.0889862 -2.37326
-2.5207365 -1.89824
-9.8378093 -4.0321
0.695562 -9.06796
0.2064454 1.849782
-1.8750774 1.158984
1.1751895 5.64904
-0.6297907 5.870312
-1.7535026 -10.6418
-5.3706886 3.796452
-2.3425774 -7.75373
1.0949303 -2.1645
-6.601591 9.539445
4.3445698 2.240785
-1.7947641 2.880266
-0.0776119 -1.83422
-0.6293166 0.83051
-4.8969915 -5.53914
2.3144333 2.136026
-1.8117749 -2.68507
-2.8260713 -11.5084
-1.129052 -6.73868
-2.4497259 -3.0306
-6.2339904 6.313874
-6.6296652 -6.71759
4.3708678 1.237768
-0.890847 2.612765
-0.7710563 -1.71815
2.0458702 -3.88667
-3.5330277 -6.83088
-1.0050562 5.820976
-4.3541368 -11.2836
-0.962748 0.074784
2.805293 -4.27134
5.0263293 -11.4895
-3.862118 -4.11209
3.0254621 -0.10239
-4.0143039 2.992369
-0.7932719 1.346866
-4.3827061 2.767718
-0.2974277 -1.26934
9.2085314 3.182633
-14.8373551 -6.8514
-4.7012557 0.829949
3.2820354 3.910262
2.4227688 -2.39648
-8.0264276 -9.28187
2.8257494 -2.61224
-3.2070853 0.164866
0.1412099 2.336446
-2.8085928 2.770362
-6.9289692 -5.66349
-4.1161351 -3.46087
-0.5579953 0.4038
0.0456535 0.838696
0.4926913 -3.98521
7.1942027 -7.59267
-2.3507502 0.208941
-6.2247442 0.075337
-6.4125236 2.337252
-0.6234384 7.880469
-2.0183142 -1.00322
2.1622125 -3.02613
-4.4688356 -9.27966
-0.3951692 3.607007
3.1918153 0.536736
2.9871983 -0.15563
3.1423024 4.624485
0.475913 5.282662
-2.234908 0.582752
1.731291
-0.7646331 8.439561
-15.7137488 -2.91457
-3.2481381 4.5167
7.1764111 -4.7472
0.3181596 -0.33106
3.1241795 7.760302
0.9688002 0.491614
-6.0979401 1.941807
-4.6284825 -7.51324
-1.3531931 -0.86409
1.26951 -4.4063
-0.3724952 -5.02639
-7.6311031 -8.01373
-0.4800474 6.701618
5.1983873 -1.44395
-2.8494264 2.122709
-0.6012605 -1.88085
-0.7092913 -3.28002
-3.7965366 -2.94921
-6.0552716 3.744603
11.9802199 -2.40617
6.2141919 6.01789
4.0561693 -3.83861
-1.623868 -2.50994
-11.8396674 3.024526
1.9338397 4.138982
-9.9237134 -0.80119
-3.5202661 -4.05715
-5.0251974 -2.24683
-5.4983941 -1.67279
-1.8573165 3.207962
-1.4762388 1.664685
3.1701793 0.206015
6.886622 -6.74688
-0.345707 -3.93421
0.3240495 -4.72459
4.806383 -5.86403
-6.5607706 11.28332
-0.7348318 3.59821
-5.25606 0.616881
-5.2173534 1.292299
2.9398239 -0.97775
-4.1348206 -1.64753
-2.0451112 -7.55368
0.1801881 0.624283
-2.4501196 3.11678
-4.7174425 -17.1385
-6.808145 -1.17196
-1.1420789 -1.2743
-0.2482968 -2.55457
0.2028957 11.45774
-8.3423952 2.717381
-8.2862535 1.3774
-3.8369365 2.629144
-9.0331927 -0.18937
-5.7770964 -0.4566
2.0495111 0.20448
-8.2252479 -6.00943
0.1576227 -9.38142
0.9925095 8.966435
3.719399 0.180837
1.1813747 0.492192
6.2759397 3.139591
-2.5159754 -0.22738
-3.9122932 -4.91527
-2.5786361 6.190169
1.3628201 2.913467
-5.5145886 -1.17024
-7.3247094 2.255335
-6.7054783 -3.85975
-0.3584976 -5.36813
1.8171054 -8.28573
2.0699217 -0.14278
0.9767156 -14.2477
-10.3163483 2.048051
-12.2431986 -10.3251
-0.0219754 -2.49404
-8.3073963 1.686435
-11.2258878 -0.33062
-6.4214187 0.780694
0.8178172 -2.11062
0.8861463 -0.08466
-5.6689013 -3.49913
-2.8512553 -2.81796
-4.6007908 2.008555
-4.3196666 -5.25072
3.9943866 1.622848
0.1637638 1.684117
-1.7775848 -5.07716
0.4400552 -4.70374
5.5348568 1.126762
2.4332177 -1.62769
-2.5372016 -12.9012
1.4489855 4.477948
3.9595523 -1.91513
3.7060067 1.132025
1.6192715 7.465044
-3.2990431 -4.17324
5.7521376 0.383871
4.5824325 3.119742
-5.986428 -4.04476
-2.7160663 -0.6706
4.7357418 1.062954
3.0579472 1.71928
2.5474543 2.634931
-7.0178901 -2.43601
3.4114273 6.587094
2.3137731 -0.55004
2.6764859 3.225261
-1.9435206 1.087141
-1.6361526 -4.1553
-1.3745129 1.170741
0.489777 2.490676
0.2819472 2.970074
-2.8797525 4.007218
-3.1051498 0.975139
8.2444426 -8.34104
3.8681968 -8.06503
-2.6720186 3.505279
-2.5913489 -9.12681
0.4573374 3.068595
1.9603745 -2.88406
-7.3868417 -5.76214
3.2100452 -3.71941
7.8072373 -1.66116
-5.7565762 4.17197
-2.255004 2.999164
-2.3457 3.553717
0.6045291 4.581446
-2.3757062 -3.06703
0.5284771 4.466503
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5.3531244
5.3257137

 

H0: Cholestrol level difference with treatment = cholestrol difference without treatment
Ha: cholestrol level difference with teatment<Cholestrol difference without treatment
t-Test: Two-Sample Assuming Unequal Variances
  Difference in chol_treatment Difference in chol_ notreatment
Mean -1.04341 -1.191918309
Variance 25.14195 24.88020654
Observations 2202 940
Hypothesized Mean Difference 0
Df 1782
t Stat 0.762967
P(T<=t) one-tail 0.222792
t Critical one-tail 1.645709
P(T<=t) two-tail 0.445584
t Critical two-tail 1.961296
The p value is more than 0.05 which means there is not sufficient statistical evidence to reject the null hypotheis
Hence it can be inferred that treatment is not effective in lowering cholestrol level