8. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct a 90% confidence interval about u if the sample size, n, is 29. (b) Construct a 90% confidence interval about u if the sample size, n, is 19. (c) Construct a 70% confidence interval about u if the sample size, n, is 29. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? 14 Click the icon to view the table of areas under the t-distribution.
8. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation, s, is found to be 10. (a) Construct a 90% confidence interval about u if the sample size, n, is 29. (b) Construct a 90% confidence interval about u if the sample size, n, is 19. (c) Construct a 70% confidence interval about u if the sample size, n, is 29. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? 14 Click the icon to view the table of areas under the t-distribution.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:11/17/21, 9:38 AM
HW 9.2 (13 Quest)-Shams Ismael
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
12.706
4.303
3.182
2.776
2.571
31.821
6.965
4.541
3.747
318.30
22.32
10.21
7.17
5.89
1
1.376
1.061
1.963
1.386
1.250
1.190
3.078
1.886
1.638
1.533
1.476
6.314
2.920
2.353
15.894
4.849
3.482
2.999
2.757
63.657
9.925
5.841
4.604
4.032
127.321
14.089
1.000
0.816
0.765
0.741
0.727
0.978
0.941
7.453
2.132
2.015
5.598
4.773
0.920
1.156
3.365
3.707
3.499
3.355
3.250
6.
0.718
0.711
4.317
4.029
0.906
1.134
1.440
1.943
2.447
2.612
3.143
5.20
0.896
0.889
0.883
0.879
1.119
1.108
2.365
2.306
2.262
2.228
7
2.517
1.415
1.397
1.383
1.372
1.895
2.998
4.78
4.50
4.29
4.14
8
0.706
1.860
2.449
2.896
3.833
3.690
2.821
2.764
0.703
1.833
1.812
2.398
2.359
9.
1.100
10
0.700
1.093
3.169
3.581
11
12
13
14
15
0.697
0.695
0.694
0.692
0.691
1.363
1.356
1.350
1.345
1.341
4.02
3.93
3.85
3.78
0.876
1.088
1.083
1.796
2.201
2.328
2.718
2.681
2.650
3.106
3.055
3.012
2.977
2.947
3.497
3.428
3.372
3.326
3.286
0.873
0.870
1.782
1.771
2.179
2.160
2.303
2.282
2.264
1.079
1.076
1.074
2.145
2.131
2.624
2.602
0.868
1.761
0.866
1.753
2.249
3.73
1.071
1.069
1.337
1.746
2.235
2.583
2.567
2.552
2.539
2.528
2.921
2.898
2.878
3.68
3.64
3.61
16
0.690
0.865
2.120
3.252
0.689
0.688
0.863
0.862
0.861
0.860
17
1.333
1.740
2.110
2.101
2.093
2.224
3.222
1.067
1.066
1.064
3.197
3.174
3.153
18
1.330
1.734
2.214
1.729
1.725
19
0.688
0.687
1.328
2.205
2.197
2.861
2.845
3.57
20
1.325
2.086
3.55
1.323
1.321
1.319
3.135
3.119
3.104
3.091
21
0.859
0.858
0.858
0.857
1.721
1.717
1.714
1.711
2.080
2.189
2.518
2.831
2.819
2.807
2.797
3.52
3.50
3.48
3.46
3.45
0.686
1.063
1.061
2.074
2.069
2.064
2.183
2.177
2.172
2.508
2.500
2.492
22
0.686
23
0.685
1.060
1.059
1.058
24
0.685
1.318
25
0.684
0.856
1.316
1.708
2.060
2.167
2.485
2.787
3.078
0.684
0.684
0.683
0.683
1.058
1.057
1.056
1.706
1.703
1.701
26
2.056
2.162
2.479
0.856
0.855
0.855
0.854
0.854
1.315
1.314
1.313
1.311
1.310
2.779
3.067
3.43
3.42
3.40
3.39
3.38
2.052
2.048
2.473
2.467
3.057
3.047
3.038
27
2.158
2.154
2.150
2.771
2.763
2.756
28
29
1.055
1.699
2.045
2.462
30
0.683
1.055
1.697
2.042
2.147
2.457
2.750
3.030
0.682
0.682
0.853
0.853
0.853
0.852
31
32
1.054
1.054
1.309
1.309
2.144
2.141
2.040
2.453
2.449
2.744
2.738
3.022
3.015
1.696
3.37
2.037
2.035
2.032
2.030
3.36
3.35
3.34
3.34
1.694
0.682
0.682
0.682
1.053
1.052
1.052
1.308
33
34
35
1.692
1.691
1.690
2.138
2.136
2.133
2.445
2.441
2.733
2.728
3.008
3.002
2.996
1.307
0.852
1.306
2.438
2.724
36
37
38
39
40
2.028
2.026
2.024
2.023
2.021
0.681
0.852
0.851
0.851
0.851
0.851
1.052
1.051
1.051
1.050
1.306
1.305
1.304
1.304
1.688
2.131
2.129
2.127
2.125
2.434
2.431
2.429
2.719
1.687
1.686
1.685
1.684
2.990
2.985
2.980
2.976
2.971
3.33
3.32
3.31
3.31
3.30
0.681
2.715
2.712
0.681
0.681
2.426
2.423
2.708
2.704
0.681
1.050
1.303
2.123
2.109
2.099
2.093
3.26
3.23
3.21
3.19
3.18
0.849
1.047
1.299
1.296
1.294
1.292
1.676
2.009
2.403
90
2.381
2.678
2.937
2.915
2.899
2.887
2.878
50
60
0.679
0.679
0.848
00
2.660
70
0.678
0.847
1.044
1.667
1.994
2.648
0.678
0.677
1.043
1.042
1.664
1.662
2.088
2.084
2.374
2.368
80
0.846
1.990
2.639
2.632
90
0.846
1.291
1.987
1.290
1.282
0.677
100
1000
0.845
0.842
1.042
1.037
1.036
1.660
1.984
1.962
2.081
2.056
2.364
2.330
2.626
2.581
2.871
3.17
3.09
2.813
2.807
0.675
1.646
0.674
0.842
1.282
1.645
1.960
2.054
2.326
2.576
3.09
df
0.25
0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
22/28
Transcribed Image Text:8. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to
be 110, and the sample standard deviation, s, is found to be 10.
(a) Construct a 90% confidence interval about u if the sample size, n, is 29.
(b) Construct a 90% confidence interval about µ if the sample size, n, is 19.
(c) Construct a 70% confidence interval about µ if the sample size, n, is 29.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
14
Click the icon to view the table of areas under the t-distribution.
(a) Construct a 90% confidence interval about u if the sample size, n, is 29.
Lower bound:
Upper bound:
(Use ascending order. Round to one decimal place as needed.)
(b) Construct a 90% confidence interval about µ if the sample size, n, is 19.
Lower bound:
; Upper bound:
(Use ascending order. Round to one decimal place as needed.)
How does decreasing the sample size affect the margin of error, E?
O A. As the sample size decreases, the margin of error increases.
O B. As the sample size decreases, the margin of error decreases.
C. As the sample size decreases, the margin of error stays the same.
(c) Construct a 70% confidence interval about u if the sample size, n, is 29.
Lower bound:
; Upper bound:
(Use ascending order. Round to one decimal place as needed.)
Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin
of error, E?
O A. As the level of confidence decreases, the size of the interval decreases.
O B. As the level of confidence decreases, the size of the interval stays the same.
C. As the level of confidence decreases, the size of the interval increases.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
A. Yes, the population needs to be normally distributed.
O B. No, the population does not need to be normally distributed.
OC. No, the population needs to be normally distributed.
O D. Yes, the population does not need to be normally distributed.
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