To test H0: μ=100 versus H1: μ≠100, a simple random sample size of n=23 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). (a) If x=105 and s=9.1, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical values. (Use a comma to separate answers as needed. Round to three decimal places as needed.)
To test H0: μ=100 versus H1: μ≠100, a simple random sample size of n=23 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). (a) If x=105 and s=9.1, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical values. (Use a comma to separate answers as needed. Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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To test H0: μ=100 versus H1: μ≠100, a simple random
(a) If x=105 and s=9.1, compute the test statistic.
(b) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical values. (Use a comma to separate answers as needed. Round to three decimal places as needed.)
Transcribed Image Text:t-Distribution Area in Right Tail
t-Distribution
Area in Right Tail
df
0.25
0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
0.0005
df
3.078
15.894
4.849
3.482
2.999
2.757
1.376
1.963
31.821
63.657
318.309
636.619
31.599
12.924
8.610
6.869
1
1.000
6.314
12.706
127.321
1
2.920
2.353
2.132
2.015
9.925
5.841
4.604
14.089
7.453
5.598
4.773
22.327
10.215
7.173
5.893
0.816
1.061
0.978
0.941
1.386
1.886
4.303
6.965
2
1.638
1.533
3
0.765
1.250
1.190
1.156
3.182
2.776
4.541
3.747
3
4
4
0.741
0.727
0.920
1.476
2.571
3.365
4.032
0.718
7
0.711
8
0.706
0.703
1.943
1.895
1.860
1.833
1.812
5.208
4.785
4.501
4.297
1.134
2.447
2.612
4.317
5.959
5.408
5.041
0.906
1.440
1.415
1.397
1.383
1.372
3.143
2.998
2.896
2.821
3.707
6.
0.896
0.889
0.883
1.119
1.108
1.100
1.093
2.517
2.449
2.398
2.359
3.499
3.355
3.250
3.169
4.029
3.833
3.690
3.581
2.365
2.306
7
8
2.262
2.228
4.781
4.587
9
10
0.700
0.879
2.764
4.144
10
0.876
0.873
0.870
1.088
1.363
1.796
1.782
1.771
1.761
1.753
3.106
3.055
3.012
3.497
3.428
3.372
4.025
3.930
3.852
3.787
3.733
11
4.437
0.697
0.695
0.694
0.692
2.201
2.179
2.160
2.328
2.718
11
12
13
1.083
1.079
1.356
1.350
2.303
2.282
2.264
2.681
2.650
2.624
2.602
4.318
4.221
12
13
2.145
2.131
2.977
2.947
14
0.868
1.076
1.345
3.326
3.286
4.140
14
15
0.691
0.866
1.074
1.341
2.249
4.073
15
3.686
3.646
3.610
3.579
3.552
16
17
0.690
0.689
0.688
0.688
0.687
0.865
0.863
0.862
1.071
1.069
1.067
1.337
1.333
1.330
1.328
1.746
1.740
2.120
2.110
2.235
2.224
2.214
2.205
2.583
2.567
2.921
2.898
2.878
3.252
3.222
4.015
3.965
3.922
16
17
1.734
1.729
18
2.101
2.552
3.197
18
3.883
3.850
19
0.861
1.066
2.093
2.539
2.861
3.174
19
20
0.860
1.064
1.325
1.725
2.086
2.197
2.528
2.845
3.153
20
0.686
0.686
0.685
0.685
0.859
0.858
0.858
21
22
1.063
1.061
1.323
1.321
1.319
1.721
1.717
2.080
2.074
2.189
2.183
2.177
2.172
2.167
2.518
2.508
3.527
3.505
3.485
2.831
2.819
3.135
3.119
3.819
3.792
3.768
3.745
3.725
21
22
1.060
1.059
1.058
2.069
2.064
2.060
2.500
2.492
2.485
2.807
2.797
2.787
23
1.714
3.104
23
0.857
0.856
3.091
3.078
3.467
3.450
24
1.318
1.711
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25
0.684
1.316
1.708
25
26
0.684
0.856
1.058
1.315
1.706
2.056
2.162
2.479
2.779
3.067
3.435
3.707
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Transcribed Image Text:t-Distribution Area in Right Tail
0.688
0.687
1.328
1.325
2.093
2.086
1.729
2.205
2.197
2.539
2.528
19
0.861
0.860
1.066
2.861
3.174
3.579
3.883
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20
1.064
1.725
2.845
3.153
3.552
3.850
20
0.859
0.858
0.858
1.063
1.061
1.060
1.059
1.058
1.323
1.321
1.319
2.080
2.074
2.069
2.064
2.060
2.518
2.508
2.500
2.492
2.485
21
22
0.686
0.686
1.721
1.717
1.714
2.189
2.183
2.177
2.172
2.167
2.831
2.819
2.807
2.797
2.787
3.135
3.119
3.527
3.505
3.485
3.467
3.450
3.819
3.792
3.768
21
22
0.685
0.685
0.684
3.104
3.091
23
23
0.857
0.856
1.318
1.316
1.711
1.708
24
3.745
24
25
3.078
3.725
25
1.706
1.703
1.058
1.057
1.056
1.055
1.055
2.056
2.052
2.048
2.479
2.473
0.856
0.855
0.855
3.435
3.421
3.408
3.396
3.385
26
0.684
1.315
2.162
2.779
3.067
3.057
3.047
3.038
3.030
3.707
26
1.314
1.313
1.311
1.310
2.158
2.154
2.150
2.147
27
0.684
2.771
3.690
27
0.683
0.683
0.683
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1.701
2.467
2.763
3.674
3.659
3.646
28
29
30
0.854
0.854
1.699
1.697
2.045
2.042
2.462
2.457
2.756
2.750
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30
1.696
1.694
1.692
1.691
1.690
3.633
3.622
1.054
2.453
3.022
3.015
3.375
3.365
3.356
3.348
3.340
31
0.682
0.853
0.853
0.853
0.852
0.852
1.309
2.040
2.037
2.035
2.032
2.030
2.144
2.141
2.138
2.136
2.133
2.744
2.738
2.733
2.728
2.724
31
0.682
0.682
0.682
0.682
32
1.054
1.309
2.449
2.445
2.441
2.438
32
1.053
1.052
1.052
33
1.308
3.008
3.611
33
34
35
1.307
1.306
3.002
2.996
3.601
3.591
34
35
2.028
2.026
2.024
2.023
2.021
1.052
2.131
2.719
2.715
2.712
2.708
2.704
2.990
2.985
2.980
2.976
3.582
3.574
36
0.681
0.852
0.851
0.851
0.851
1.306
1.688
1.687
1.686
1.685
1.684
2.434
3.333
36
3.326
3.319
3.313
3.307
37
0.681
1.051 1.305
2.129 2.431
37
38
39
0.681
0.681
0.681
1.051
1.050
1.050
1.304
1.304
3.566
3.558
3.551
2.127
2.429
38
39
2.125 2.426
2.423
2.123
40
0.851
1.303
2.971
40
0.849
0.848
0.847
0.846
0.846
1.047 1.299
2.009
2.000
2.403
2.390
2.381
2.374
2.368
2.678
2.660
2.648
2.639
2.632
50
0.679
1.676
3.261
2.109
2.099
2.093
2.088
2.084
2.937
3.496
50
0.679
1.045 1.296
1.67
2.91.
3.460
3.23
3.211
3.195
60
60
0.678
0.678
0.677
3.435
3.416
3.402
70
1.044 1.294
1.043 1.292
1.042 1.291
1.667
1.664
1.662
1.994
1.990
2.899
2.887
2.878
70
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90
1.987
3.183
90
100
1000
1.290
1.282
1.282
2.626
2.581
2.576
3.174
3.098
3.090
0.845
1.660
1.646
1.645
2.081
3.390
0.677
0.675
0.674
1.042
1.984
1.962
1.960
2.364
2.330
2.326
2.871
2.813
2.807
100
0.842
0.842
1.037
1.036
2.056
2.054
3.300 1000
3.291 z
df
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