A random sample of 28 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯x¯ = 790 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student’s t. (a) Construct an interval estimate of μ with 99% confidence. (b) Construct an interval estimate of μ with 99% confidence, assuming that s = 30. (c) Construct an interval estimate of μ with 99% confidence, assuming that s = 60. (Round your answers to 3 decimal places.)
A random sample of 28 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯x¯ = 790 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student’s t. (a) Construct an interval estimate of μ with 99% confidence. (b) Construct an interval estimate of μ with 99% confidence, assuming that s = 30. (c) Construct an interval estimate of μ with 99% confidence, assuming that s = 60. (Round your answers to 3 decimal places.)
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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A random sample of 28 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯x¯ = 790 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student’s t.
(a) Construct an
(b) Construct an interval estimate of μ with 99% confidence, assuming that s = 30.
(c) Construct an interval estimate of μ with 99% confidence, assuming that s = 60. (Round your answers to 3 decimal places.)
Transcribed Image Text:APPENDIX
STUDENT'St CRITICAL VALUES
This table shows the t-value that defines the area for the stated degrees of freedom (d.f.).
Confidence Level
Confidence Level
.80
.90
.95
.98
.99
.80
.90
.95
.98
.99
Significance Level for Two-Tailed Test
Significance Level for Two-Tailed Test
.20
.10
.05
.02
.01
.20
.10
.05
.02
.01
Significance Level for One-Tailed Test
Significance Level for One-Tailed Test
d.f.
.10
.05
.025
.01
.005
d.f.
.10
.05
.025
.01
.005
1
3.078
6.314
12.706
31.821
63.657
36 1.306
1.688
2.028
2.434
2.719
1.886
2.920
4.303
6.965
9.925
37
1.305 1.687 2.026
2.431
2.715
3.
1.638
2.353
3.182
4.541
5.841
38
1.304
1.686 2.024
2.429
2.712
4
1.533
2.132
2.776
3.747
4.604
39
1.304
1.685
2.023
2.426
2.708
1.476
2.015
2.571
3.365
4.032
40
1.303
1.684
2.021
2.423
2.704
6
1.440
1.943
2.447
3.143
3.707
41
1.303
1.683
2.020
2.421
2.701
7
1.415
1.895
2.365
2.998
3.499
42 1.302
1.682
2.018
2.418
2.698
8
1.397
1.860
2.306
2.896
3.355
43
1.302
1.681
2.017
2.416
2.695
9
1.383
1.833
2.262
2.821
3.250
44
1.301
1.680
2.015
2.414
2.692
10
1.372
1.812
2.228
2.764
3.169
45
1.301
1.679
2.014
2.412
2.690
11
1.363
1.796
2.201
2.718
3.106
46
1.300
1.679
2.013
2.410
2.687
12
1.356
1.782
2.179
2.681
3.055
47
1.300
1.678
2.012
2.408
2.685
13
1.350
1.771
2.160
2.650
3.012
48
1.299
1.677
2.011
2.407
2.682
14
1.345
1.761
2.145
2.624
2.977
49 1.299
1.677
2.010
2.405
2.680
15
1.341
1.753
2.131
2.602
2.947
50
1.299
1.676
2.009
2.403
2.678
16
1.337
1.746
2.120
2.583
2.921
55 1.297 1.673
2.004
2.396
2.668
17
1.333
1.740
2.110
2.567
2.898
60 1.296
1.671
2.000
2.390 2.660
18
1.330
1.734
2.101
2.552
2.878
65
1.295
1.669
1.997
2.385
2.654
19
1.328
1.729
2.093
2.539
2.861
70 1.294
1.667
1.994
2.381
2.648
20
1.325
1.725
2.086
2.528
2.845
75 1.293
1.665
1.992
2.377
2.643
21 1.323
1.721
2.080
2.518
2.831
80 1.292
1.664
1.990
2.374
2.639
22
1.321
1.717
2.074
2.508
2.819
85
1.292
1.663
1.988
2.371
2.635
23
1.319
1.714
2.069
2.500
2.807
90
1.291 1.662
1.987
2.368
2.632
24
1.318
1.711
2.064
2.492
2.797
95
1.291
1.661
1.985
2.366
2.629
25
1.316
1.708
2.060
2.485
2.787
100
1.290
1.660
1.984
2.364
2.626
26
1.315
1.706
2.056
2.479
2.779
110
1.289 1.659
1.982
2.361
2.621
27
1.314
1.703
2.052
2.473
2.771
120
1.289
1.658
1.980
2.358
2.617
28
1.313
1.701
2.048
2.467
2.763
130
1.288
1.657
1.978
2.355
2.614
29
1.311
1.699
2.045
2.462
2.756
140
1.288 1.656
1.977
2.353
2.611
30
1.310
1.697
2.042
2.457
2.750
150
1.287
1.655
1.976
2.351
2.609
31
1.309
1.696
2.040
2.453
2.744
1.282
1.645
1.960
2.326
2.576
00
32
1.309
1.694
2.037
2.449
2.738
33
1.308
1.692
2.035
2.445
2.733
34
1.307
1.691
2.032
2.441
2.728
35
1.306
1.690
2.030
2.438
2.724
Note: As n increases, critical values of Student's t approach the z-values in the last line of this table. A common rule of thumb is to use z when n
> 30, but that is not conservative.
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