Problem 3: Suppose that you are testing the following hypotheses where the variance is unknown:,u = 100 H144 > 100 The sample size is n = 10....
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How to find out the p-value with t table?q3.png

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Problem 3: Suppose that you are testing the following hypotheses where the variance is
unknown: H0:,u = 100
H144 > 100 The sample size is n = 10. Using the ttable, find bounds on the P-value for the following values
of the test statistic. a) r0=2.75
b) 130:1.86
c) to: — 2.05
d) to: — 1.86 Remark: the degree of freedom, v = n — 1

t-table.png

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Appendix
APPENDIX IV
Percentage Points of the t Distribution
av
0.40
0.25
0.025
0.01
0.005
0.0025
0.001
0.0005
0.325
1.000
3.078
6.314
12.706
63.657
127.32
318.31
0.289
0.816
1.886
2.920
4.303
6.965
9.925
14.089
23.326
31.598
0.765
1.638
2.353
3.182
4.541
5.841
12.924
0.271
0.741
1.533
2.132
2.776
3.747
4.604
5.598
7.173
8.610
1.476
2.571
4.032
4.773
5.893
6.869
0.727
1.440
1.943
2.447
3.143
3.707
4.317
5.208
5.959
0.711
1.415
1.895
2.365
2.998
5.408
0.706
2.306
2.896
3.355
3.833
4.501
5.041
0.703
1.383
1.833
2.262
2.821
3.250
3.690
4.297
4.781
10 0.260
0.700
1.372
1.812
2.228
2.764
3.581
4.144
4.587
11 0.260
0.697
1.363
1.796
2.20
3.106
4.025
4.437
12 0.259
0.695
1.782
2.179
2.681
3.055
3.428
3.930
4.318
0.694
1.350
2.160
2.650
3.012
3.372
3.852
14 0.258
0.692
1.345
1.761
2.145
2.624
2.977
15 0.258
3.326
3.787
4.140
0.691
2.131
2.947
3.286
16 0.258
4.073
0.690
1.337
1.746
2.120
2.583
2.921
3.252
3.686
4.015
1.333
2.110
2.898
3.222
3.646
18 0.257
3.965
0.688
1.330
1.734
2.101
2.552
2.878
3.197
19 0.257
3.610
3.992
0.688
1.328
2.093
2.539
2.861
3.174
20 0.257
3.579
3.883
0.687
1.325
1.725
2.086
2.528
2.845
3.153
0.686
3.552
3.850
1.721
2.080
2.518
2.831
3.135
22 0.256
3.527
3.819
0.686
1.321
1.717
2.074
2.508
2.819
3.119
23 0.256
3.505
3.792
0.685
1.319
2.069
2.500
2.807
3.104
24 0.256
3.485
3.767
0.685
1.711
2.064
2.492
2.797
0.684
3.467
3.745
2.060
2.485
2.787
3.078
26 0.256
3.450
3.725
0.684
1.315
1.706
2.056
2.479
2.779
3.067
27 0.256
3.435
3.707
0.684
1.703
2.052
2.473
2.771
3.057
3.421
3.690
0.683
1.313
1.701
2.048
2.763
3.047
3.408
0.683
3.674
1.311
1.699
2.045
2.462
2.756
3.038
3.396
30 0.256
3.659
0.683
1.697
2.042
2.457
2.750
3.030
3.385
3.646
0.681
1.684
2.021
2.423
2.704
2.971
3.307
3.551
1.296
1.671
2.000
2.660
2.915
120 0.254
3.232
3.460
0.677
1.289
1.658
1.980
2.358
2.617
2.860
3.160
3.373
0.253
1.282
1.645
1.960
3.090
3.291
v = degrees of freedom
Source: Adapted with permission from Biometrika Tables for Statisticians, Vol. 1, 3rd ed., by E. S. Pearson and H. O. Hartley,
Cambridge University Press, Cambridge, 1966.

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