A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about μ if the sample size, n, is 18. Lower bound:___ Upper bound:____ (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about μ if the sample size, n, is 29. lower bound ___ upper bound___ (Use ascending order. Round to one decimal place as needed.) (c) Construct a 99% confidence interval about μ if the sample size, n, is
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about μ if the sample size, n, is 18. Lower bound:___ Upper bound:____ (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about μ if the sample size, n, is 29. lower bound ___ upper bound___ (Use ascending order. Round to one decimal place as needed.) (c) Construct a 99% confidence interval about μ if the sample size, n, is
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10.
(a) Construct a 98% confidence interval about μ if the sample size, n, is
18.
Lower bound:___
Upper bound:____ (Use ascending order. Round to one decimal place as needed.)
Upper bound:____ (Use ascending order. Round to one decimal place as needed.)
(b) Construct a 98% confidence interval about μ if the sample size, n, is
29.
lower bound ___
upper bound___ (Use ascending order. Round to one decimal place as needed.)
(c) Construct a 99% confidence interval about μ if the sample size, n, is
18.
Lower bound ___
Upper bound___ (Use ascending order. Round to one decimal place as needed.)
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Transcribed Image Text:Table of t-Distribution Areas
318.309
22.327
10.215
7.173
1
1.000
1.376
1.061
0.978
1.963
1.386
1.250
1.190
1.156
3.078
1.886
1.638
1.533
1.476
6.314
12.706
4.303
3.182
15.894
31.821
63.657
127.321
636.619
6.965
4.541
3.747
3.365
0.816
2.920
2.353
2.132
2.015
4.849
3.482
2.999
2.757
9.925
5.841
4.604
4.032
14.089
7.453
5.598
4.773
31.599
12.924
3
0.765
4
0.741
0.941
2.776
8.610
6.869
5
0.727
0.920
2.571
5.893
0.718
0.711
2.612
2.517
0.906
1.134
1.440 1.943
2.447
2.365
2.306
2.262
3.143
3.707
4.317
5.208
4.785
5.959
5.408
5.041
4.781
0.896
2.998
1.415 1.895
1.108 1.397 1.860
1.383
1.372
1.119
2.449
2.398
2.359
3.499
3.355
3.250
3.169
4.029
3.833
3.690
4.501
4.297
8
0.706
0.703
0.700
0.889
0.883
0.879
2.896
2.821
9
1.100
1.833
10
1.093
1.812
2.228
2.764
3.581
4.144
4.587
2.201
2.179
2.160
2.145
3.497
3.428
3.372
4.025
3.930
3.852
3.787
3.733
0.876
0.873
11
1.088
0.697
0.695
1.363
1.356
1.350
1.345
1.341
1.796
2.328
2.303
2.718
3.106
3.055
3.012
2.977
2.947
4.437
4.318
4.221
1.782
2.681
2.650
12
1.083
1.079
13
2.282
2.264
2.249
0.694
0.870
1.771
14
0.692
1.076
1.761
2.624
3.326
3.286
4.140
4.073
0.868
15
0.691
0.866
1.074
1.753
2.131
2.602
2.120
2.110
2.101
2.235
2.224
2.583
2.567
2.552
2.539
2.528
0.690
1.071
1.069
1.337
2.921
2.898
3.252
4.015
3.965
16
0.865
0.863
0.862
1.746
3.686
3.646
3.610
3.579
3.552
17
0.689
0.688
0.688
0.687
1.333
1.740
3.222
3.197
3.174
3.153
3.922
3.883
3.850
2.878
2.861
18
1.067
1.330
1.734
2.214
1.066
1.064
19
0.861
1.328
1.729
2.093
2.205
20
0.860
1.325
1.725
2.086
2.197
2.845
1.063
1.061
1.060
1.323 1.721
1.321
2.518
2.508
2.500
2.492
2.485
21
0.686
0.859
2.080
2.189
2.831
3.135
3.119
3.104
3.091
3.078
3.527
3.819
0.858
0.858
2.183
2.177
2.172
22
2.074
3.792
0.686
0.685
0.685
1.717
2.819
3.505
3.485
1.714
23
24
1.319
1.318
2.069
2.064
2.060
2.807
3.768
0.857
0.856
1.059
1.711
2.797
3.467
3.745
25
0.684
1.058
1.316
1.708
2.167
2.787
3.450
3.725
2.162
2158.
3.067
3.435
3 421
26
0.856
0 85.
1.058
1.315 1.706
1 314.
1 703.
2.056
2.479
2 473.
2.779
2 771.
0.684
3.707
27
0 684
1 057
2052
3.057
3.690
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Transcribed Image Text:i Table of t-Distribution Areas
2.056
1.315
1.314
3.067
3.057
3.047
3.038
26
0.856
2.779
0.684
0.684
1.058
1.057
1.056
1.055
1.055
1.706
2.162
2.479
3.435
3.707
0.855
0.855
0.854
27
1.703
2.052
2.158
2.154
2.150
2.147
2.473
2.771
3.421
3.408
3.396
3.385
3.690
28
29
0.683
0.683
0.683
1.313
1.311
1.701
1.699
2.048
2.045
2.042
2.467
2.462
2.457
2.763
2.756
3.674
3.659
30
0.854
1.310
1.697
2.750
3.030
3.646
1.054
1.054
1.053
1.052
1.052
3.375
3.365
3.356
3.348
3.340
0.682
1.309
1.696
2.744
2.738
2.733
2.728
2.724
31
32
0.853
2.040
2.144
2.141
2.138
2.136
2.133
2.453
2.449
3.022
3.633
3.622
3.611
1.694
1.692
1.691
1.690
3.015
3.008
3.002
2.996
0.853
1.309
2.037
0.682
0.682
33
34
0.853
0.852
1.308
1.307
2.035
2.032
2.030
2.445
2.441
2.438
0.682
3.601
35
0.682
0.852
1.306
3.591
2.028
2.026
36
0.852
1.052 1.306
1.305
1.304
2.131
3.333
3.326
3.319
3.313
3.307
3.582
3.574
3.566
0.681
1.688
2.434
2.431
2.719
2.990
2.985
37
38
39
2.715
2.712
2.708
0.681
0.851
0.851
0.851
1.051
1.051
1.050
1.687
2.129
1.686
1.685
1.684
2.127
2.125
2.123
0.681
2.024
2.429
2.426
2.980
2.976
2.971
2.023
3.558
3.551
0.681
1.304
40
0.681
0.851
1.050
1.303
2.021
2.423
2.704
2.937
2.915
3.496
3.460
3.435
3.416
0.679
0.679
0.849
1.047
1.676
2.009
2.000
1.994
2.678
50
60
1.299
1.296
2.109
2.099
2.093
2.088
2.084
3.261
3.232
3.211
2.403
2.390
1.045
1.044
0.848
1.671
2.660
70
0.678
0.847
1.294
1.667
2.381
2.648
2.639
2.632
2.899
1.043
1.042
2.887
80
90
0.678
0.677
1.664
1.662
3.195
3.183
0.846
1.292
1.291
1.990
2.374
2.368
0.846
1.987
2.878
3.402
1.042
1.037
1.290
1.282
1.282
2.626
2.581
2.576
100
0.677
0.845
0.842
0.842
1.660
1.984
1.962
1.960
2.081
2.056
2.054
2.364
2.871
2.813
2.807
3.174
3.390
1000
0.675
1.646
2.330
3.098
3.300
0.674
1.036
1.645
2.326
3.090
3.291
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
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