A simple random sample of Size n is drawn. The sample mean, X, IS Tound to be 18.4, and the sample standard deviation, s, is found to be 4.1. 1 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 61. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error increases. O B. The margin of error decreases. O C. The margin of error does not change. (c) Construct a 99% confidence interval about u if the sample size, n, is 35. ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error decreases. B. The margin of error increases. C. The margin of error does not change. (d) If the sample size is 16, what conditions must be satisfied to compute the confidence interval? O A. The sample data must come from a population that is normally distributed with no outliers. B. The sample size must be large and the sample should not have any outliers. C. The sample must come from a population that is normally distributed and the sample size must be large.
A simple random sample of Size n is drawn. The sample mean, X, IS Tound to be 18.4, and the sample standard deviation, s, is found to be 4.1. 1 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 61. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error increases. O B. The margin of error decreases. O C. The margin of error does not change. (c) Construct a 99% confidence interval about u if the sample size, n, is 35. ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error decreases. B. The margin of error increases. C. The margin of error does not change. (d) If the sample size is 16, what conditions must be satisfied to compute the confidence interval? O A. The sample data must come from a population that is normally distributed with no outliers. B. The sample size must be large and the sample should not have any outliers. C. The sample must come from a population that is normally distributed and the sample size must be large.
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:1: Table of t-Distribution Areas
Area in
right tail
Table VI
t-Distribution
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11/17/21,9:38 AM
HW 9.2 (13 Quest)-Shams Ismael
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
1
1.963
3.078
6.314
2.920
12.706
15.894
4.849
31.821
6.965
4.541
63.657
9.925
5.841
4.604
127.321
14.089
7.453
5.598
4.773
318.30
22.32
10.21
7.17
5.89
1.000
1.376
0.816
0.765
0.741
1.386
1.250
1.190
1.156
4.303
3.182
2.776
2
1.061
0.978
0.941
1.886
3.482
2.999
2.757
1.638
1.533
1.476
2.353
2.132
2.015
3.747
3.365
0.727
0.920
2.571
4.032
6.
0.906
1.943
1.895
1.860
1.833
1.812
2.612
3.143
5.20
4.78
4.50
4.29
0.718
1.134
1.440
2.447
3.707
4.317
1.415
1.397
1.383
1.372
2.365
2.306
2.262
2.228
3.499
3.355
3.250
3.169
4.029
3.833
3.690
3.581
7
0.711
8
0.896
0.889
0.883
0.879
1.119
2.517
2.998
2.896
0.706
0.703
0.700
1.108
1.100
1.093
2.449
2.398
2.359
9.
2.821
10
2.764
4.14
3.106
3.055
3.012
2.977
2.947
0.697
0.876
0.873
1.088
1.083
1.363
1.356
2.201
2.179
2.160
2.328
2.303
2.282
2.264
2.249
2.718
2.681
3.497
3.428
4.02
3.93
11
1.796
1.782
1.771
12
0.695
0.694
0.692
0.691
2.650
2.624
2.602
3.372
3.326
3.85
3.78
3.73
13
0.870
0.868
0.866
1.079
1.076
1.074
1.350
1.345
1.341
1.761
1.753
14
2.145
15
2.131
3.286
1.337
1.333
1.330
0.690
0.865
0.863
0.862
0.861
2.583
2.567
3.68
3.64
3.61
16
1.071
1.746
2.120
2.235
2.224
2.921
3.252
3.222
3.197
3.174
17
0.689
1.069
1.740
2.110
2.898
1.067
1.066
1.064
2.878
2.861
2.845
18
0.688
0.688
0.687
1.734
1.729
1.725
2.101
2.214
2.552
2.539
1.328
1.325
2.205
2.197
3.57
3.55
19
2.093
2.086
20
0.860
2.528
3.153
0.859
1.063
1.323
1.321
1.319
2.080
2.074
21
0.686
2.189
1.721
1.717
2.518
2.831
3.135
3.52
3.50
3.48
0.686
0.685
0.685
0.684
22
0.858
0.858
0.857
0.856
1.061
2.183
2.508
2.819
3.119
3.104
3.091
3.078
23
1.060
1.714
2.069
2.177
2.500
2.807
2.064
2.060
2.492
2.485
3.46
3.45
1.059
24
25
2.172
2.167
2.797
2.787
1.318
1.711
1.708
1.058
1.316
0.856
1.706
1.703
2.162
2.158
2.154
2.150
2.147
26
0.684
1.058
1.057
1.056
1.315
1.314
2.056
2.479
2.473
2.467
2.462
2.457
2.779
3.067
3.43
3.42
2.771
2.763
2.756
27
0.684
0.855
0.855
0.854
0.854
2.052
2.048
2.045
2.042
3.057
28
29
30
0.683
0.683
1.313
1.311
1.701
1.699
3.047
3.038
3.40
3.39
3.38
1.055
0.683
1.055
1.310
1.697
2.750
3.030
0.682
0.682
1.309
1.309
2.453
2.449
0.853
1.054
1.696
2.040
2.037
2.035
2.032
2.030
31
2.144
2.744
3.022
3.37
0.853
0.853
2.141
2.138
2.136
2.738
2.733
2.728
2.724
3.015
3.008
3.36
3.35
3.34
3.34
32
1.054
1.053
1.052
1.694
33
0.682
0.682
0.682
1.308
1.307
1.306
1.692
2.445
34
0.852
1.691
2.441
3.002
35
0.852
1.052
1.690
2.133
2.438
2.996
36
37
38
39
40
0.681
0.681
0.681
0.681
2.719
2.715
2.712
2.708
2.704
0.852
1.052
1.051
1.051
1.050
1.306
1.305
1.688
1.687
1.686
1.685
1.684
2.028
2.026
2.024
2.023
2.021
2.131
2.434
2.990
2.985
2.980
2.976
2.971
3.33
3.32
2.129
2.127
2.125
2.431
2.429
2.426
2.423
0.851
0.851
1.304
1.304
3.31
3.31.
3.30
0.851
0.681
0.851
1.050
1.303
2.123
2.109
2.099
2.937
2.915
50
0.679
0.679
0.678
0.849
1.047
1.045
1.044
1.043
1.299
1.676
2.009
2.000
1.994
2.403
2.390
2.678
3.26
3.23
60
0.848
1.296
1.671
2.660
70
80
1.294
1.292
1.667
1.664
1.662
3.21
3.19
3.18
0.847
2.093
2.088
2.381
2.648
2.899
0.678
0.677
2.374
2.368
2.887
0.846
0.846
1.990
1.987
2.639
2.632
90
1.042
1.291
2.084
2.878
0.845
0.842
100
0.677
2.871
1.290
1.282
1.282
1.984
2.081
2.056
2.364
2.626
3.17
1.042
1.037
1.660
0.675
0.674
1.646
1.645
2.813
2.807
3.09
3.09
1000
1.962
2.330
2.581
0.842
1.036
1.960
2.054
2.326
2.576
df
0.25
0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
Area in Right Tail
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Transcribed Image Text:1. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.4, and the sample standard deviation, s,
is found to be 4.1.
1 Click the icon to view the table of areas under the t-distribution.
(a) Construct a 95% confidence interval about µ if the sample size, n, is 35.
; Upper bound:
(Use ascending order. Round to two decimal places as needed.)
Lower bound:
(b) Construct a 95% confidence interval about u if the sample size, n, is 61.
Lower bound:
; Upper bound:
(Use ascending order. Round to two decimal places as needed.)
How does increasing the sample size affect the margin of error, E?
O A. The margin of error increases.
O B. The margin of error decreases.
C. The margin of error does not change.
(c) Construct a 99% confidence interval about u if the sample size, n, is 35.
Lower bound:
Upper bound:
(Use ascending order. Round to two decimal places as needed.)
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin
of error, E?
O A. The margin of error decreases.
O B. The margin of error increases.
C. The margin of error does not change.
(d) If the sample size is 16, what conditions must be satisfied to compute the confidence interval?
O A. The sample data must come from a population that is normally distributed with no outliers.
B. The sample size must be large and the sample should not have any outliers.
C. The sample must come from a population that is normally distributed and the sample size must be large.
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