A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x, is found to be 114, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about u if the sample size, n, is 13. (b) Construct a 98% confidence interval about u if the sample size, n, is 28. (c) Construct a 99% confidence interval about u if the sample size, n, is 13.
A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x, is found to be 114, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about u if the sample size, n, is 13. (b) Construct a 98% confidence interval about u if the sample size, n, is 28. (c) Construct a 99% confidence interval about u if the sample size, n, is 13.
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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Transcribed Image Text:Area in
right tail
Table VI
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
1
0.816
0.765
4
1.963
1.386
1.250
1.190
1.156
3.078
1.886
1.638
1.533
15.894
4.849
3.482
2.999
2.757
636.619
31.599
12.924
8.610
1.376
6.314
2.920
2.353
2.132
2.015
12.706
4.303
3.182
2.776
2.571
31.821
63.657
9.925
127.321
14.089
7.453
5.598
4.773
318.309
22.327
10.215
7.173
5.893
1.000
6.965
4.541
3.747
2
1.061
0.978
0.941
0.920
3
5.841
0.741
0.727
4.604
4.032
5
1.476
3.365
6.869
0.718
0.711
0.706
0.703
0.700
1.134
1.119
1.108
1.100
1.440
1.943
1.895
1.860
1.833
1.812
2.447
2.365
2.306
2.262
2.228
4.317
4.029
3.833
3.690
3.581
6
0.906
0.896
0.889
0,883
0.879
2.612
2.517
3.143
2.998
2.896
2.821
3.707
3.499
1.415
1.397
1.383
1.372
3.355
3.250
3.169
5.208
4.785
4.501
4.297
5.959
5.408
5.041
4.781
8
2.449
2.398
2.359
9
10
1.093
2.764
4.144
4.587
0.697
0.695
1.363
1.356
1.350
1.345
1.341
2.201
2.179
3.106
3.497
2.328
2.303
2.282
2.264
2.249
11
0.876
1.088
1.796
2.718
4.025
4.437
1.782
1.771
1.761
1.753
12
0.873
0.870
0.868
0.866
1.083
2.681
3.055
3.428
3.372
3.326
3.286
3.930
3.852
3.787
3.733
4.318
13
0.694
1.079
2.160
2.650
3.012
4.221
2.145
2.131
2.977
2.947
14
1.076
1.074
2.624
2.602
0.692
4.140
15
0.691
4.073
0.690
0.689
0.688
0.688
0.687
0.865
0.863
0.862
0.861
0.860
1.746
1.740
1.734
1.729
1.725
3.252
3.222
3.197
3.174
3.153
16
1.337
1.333
1.330
1.328
1.325
2.120
2.110
2.101
2.093
2.086
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
1.071
2.921
2.898
2.878
2.861
2.845
3.686
3.646
3.610
3.579
3.552
4.015
3.965
3.922
3.883
3.850
17
1.069
1.067
1.066
1.064
18
19
20
1.063
1.061
3.135
3.119
3.104
3.091
3.078
21
0.859
0.858
0.858
1.323
1.321
1.319
1.318
1.316
1.721
1.717
2.189
2.518
2.508
2.500
2.492
2.485
3.527
3.505
3.485
3.467
3.450
0.686
2.080
0.686
0.685
0.685
0.684
2.074
2.069
2.064
2.060
2.831
2.819
2.807
2.797
2.787
3.819
3.792
3.768
3.745
3.725
22
2.183
23
24
25
1.060
1.059
1.058
1.714
2.177
1.711
1.708
2.172
2.167
0.857
0.856
0.684
0.684
0.683
0.683
0.683
0.856
0.855
0.855
0.854
0.854
1.058
1.057
1.056
1.055
1.055
1.706
1.703
1.701
1.699
1.697
2.056
2.052
2.048
2.045
2.042
2.162
2.158
2.154
2.150
2.147
2.479
2.473
2.467
2.462
2.457
2.779
2.771
2.763
2.756
2.750
3.067
3.057
3.047
3.038
3.030
3.435
3.421
3.408
3.396
3.385
3.707
3.690
3.674
3.659
3.646
26
27
28
29
30
1.315
1.314
1.313
1.311
1.310
0.853
0.853
0.853
1.054
1.054
1.053
1.052
1.052
2.040
2.037
2.035
2.032
2.030
2.144
2.141
2.453
2.449
2.445
2.441
2.438
3.022
3.015
3.008
3.375
3.365
3.356
3.348
3.340
1.309
1.696
1.694
1.692
31
0.682
2.744
2.738
2.733
3.633
3.622
3.611
32
33
34
35
0.682
0.682
0.682
0.682
1.309
1.308
0.852
0.852
1.691
1.690
2.138
2.136
2.133
1.307
2.728
3.002
2.996
3.601
1.306
2.724
3.591
2.719
2.715
2.712
2.708
2.704
3.582
3.574
3.566
36
37
0.681
0.681
0.681
0.681
0.852
0.851
0.851
0.851
0.851
1.052
1.051
1.051
1.306
1.305
1.304
1.304
1.303
1.688
2.028
2.131
2.129
2.127
2.125
2.123
2.434
2.431
2.429
2.426
2.990
2.985
2.980
3.333
3.326
3.319
1.687
2.026
1.686
1.685
1.684
2.024
2.023
38
39
40
3.558
3.551
1.050
2.976
3.313
3.307
0.681
1.050
2.021
2.423
2.971
0.679
0.679
0.678
1.047
1.045
1.044
2.009
2.000
1.994
1.990
0.849
1.676
1.671
1.667
1.664
2.403
2.390
2.381
2.374
2.937
2.915
2.899
2.887
50
60
1.299
1.296
1.294
1.292
2.109
2.678
3.261
3.232
2.099
2.093
2.088
2.660
2.648
2.639
3.496
3.460
3.435
3.416
0.848
70
0.847
3.211
3.195
80
0.678
0.846
1.043
Transcribed Image Text:A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 114, and the sample standard deviation, s, is found to be 10.
(a) Construct a 98% confidence interval about u if the sample size, n, is 13.
(b) Construct a 98% confidence interval about u if the sample size, n, is 28.
(c) Construct a 99% confidence interval about u if the sample size, n, is 13.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Click the icon to view the table of areas under the t-distribution.
(a) Construct a 98% confidence interval about u if the sample size, n, is 13.
Lower bound: ; Upper bound:
(Use ascending order. Round to one decimal place as needed.)
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