9. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s, is found to be 4.8. 15 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?
9. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s, is found to be 4.8. 15 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?
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
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Transcribed Image Text:9.
A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s,
is found to be 4.8.
15 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 µ 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 decreases.
O B. The margin of error does not change.
C. The margin of error increases.
(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 increases.
O B. The margin of error decreases.
C. The margin of error does not change.
(d) If the sample size is 12, what conditions must be satisfied to compute the confidence interval?
O A. The sample must come from a population that is normally distributed and the sample size must be large.
B. The sample data must come from a population that is normally distributed with no outliers.
O C. The sample size must be large and the sample should not have any outliers.
Transcribed Image Text:Area in
right tail
Table VI
t-Distribution
Area in Right Tail
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df
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0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
24/28
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HW 9.2 (13 Quest)-Shams Ismael
3.078
1.886
1.376
1.061
0.978
0.941
1
1.000
1.963
6.314
12.706
15.894
31.821
63.657
127.321
318.30
9.925
5.841
4.604
22.32
0.816
0.765
4
6.965
4.541
3.747
3.365
14.089
1.386
1.250
1.190
2.920
4.303
4.849
1.638
1.533
2.353
2.132
2.015
3.182
2.776
3.482
2.999
7.453
10.21
0.741
5.598
4.773
7.17
5.89
0.727
0.920
1.156
1.476
2.571
2.757
4.032
0.718
2.612
3.143
2.998
2.896
2.821
2.764
6.
7
0.711
0.906
1.134
1.119
1.108
1.100
1.093
1.440
1.415
1.397
1.943
2.447
2.365
3.707
3.499
3.355
3.250
3.169
4.317
4.029
3.833
3.690
3.581
5.20
0.896
0.889
0.883
1.895
1.860
1.833
1.812
4.78
4.50
4.29
4.14
2.517
8
0.706
9.
0.703
0.700
1.383
1.372
2.306
2.262
2.228
2.449
2.398
2.359
10
0.879
3.497
3.428
11
1.088
4.02
0.697
0.695
0.694
0.692
0.691
0.876
1.363
1.796
2.201
2.328
2.718
3.106
1.356
1.350
0.873
1.782
1.771
1.761
1.753
2.681
12
13
1.083
2.179
2.303
3.055
3.93
1.079
1.076
3.85
3.78
3.73
0.870
2.160
2.282
2.650
3.012
2.977
3.372
0.868
0.866
14
1.345
1.341
2.145
2.131
2.264
2.624
3.326
15
1.074
2.249
2.602
2.947
3.286
0.690
0.689
0.688
2.921
2.898
2.878
3.252
3.222
0.865
1.337
2.120
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
16
3.68
1.071
1.069
1.067
1.066
1.746
17
0.863
1.333
1.740
2.110
3.64
3.61
3.57
3.55
1.734
1.729
2.101
2.093
18
0.862
1.330
1.328
1.325
3.197
0.688
0.687
3.174
3.153
19
0.861
2.539
2.861
20
0.860
1.064
1.725
2.086
2.528
2.845
1.063
1.061
1.721
1.717
2.189
2.183
2.177
2.172
2.518
2.508
2.831
2.819
2.807
2.797
2.787
21
0.686
0.859
1.323
1.321
1.319
2.080
2.074
3.135
3.119
3.104
3.091
3.078
3.52
3.50
3.48
3.46
3.45
22
0.686
23
24
25
0.685
0.685
0.684
0.858
0.858
0.857
0.856
1.060
1.714
2.069
2.500
1.059
1.058
1.318
1.316
1.711
2.064
2.492
1.708
2.060
2.167
2.485
0.856
0.855
0.855
1.058
1.057
1.056
1.055
1.055
1.315
1.314
2.162
2.158
2.779
2.771
26
0.684
0.684
1.706
2.056
2.052
2.479
2.473
3.067
3.43
1.703
1.701
3.057
3.047
3.038
27
3.42
0.683
0.683
2.154
2.150
2.467
2.462
2.763
2.756
28
1.313
2.048
2.045
2.042
3.40
3.39
3.38
29
0.854
0.854
1.311
1.699
30
0.683
1.310
1.697
2.147
2.457
2.750
3.030
1.309
1.309
1.308
2.453
2.449
2.445
2.441
2.438
2.744
2.738
2.733
2.728
2.724
3.022
3.015
3.008
3.002
2.996
31
0.682
0.853
0.853
1.054
1.054
1.053
1.052
1.052
1.696
2.040
2.144
1.694
1.692
1.691
2.037
2.035
2.032
2.030
3.37
3.36
3.35
3.34
3.34
32
33
0.682
0.682
2.141
2.138
0.853
0.852
0.852
1.307
1.306
34
0.682
2.136
35
0.682
1.690
2.133
1.052
1.051
1.051
1.050
36
0.681
0.852
2.028
2.434
1.306
1.305
1.304
1.688
1.687
2.131
2.719
2.990
2.985
2.980
3.33
3.32
3.31
3.31.
3.30
37
0.681
0.851
2.026
2.129
2.431
2.715
2.024
0.681
0.681
0.681
38
0.851
2.127
2.429
2.712
1.686
1.685
39
0.851
1.304
1.303
2.023
2.021
2.125
2.426
2.708
2.976
2.971
40
0.851
1.050
1.684
2.123
2.423
2.704
0.849
0.848
0.847
1.047
1.045
1.044
1.043
1.299
2.678
2.660
2.648
2.639
2.632
50
0.679
1.676
2.009
2.109
2.099
2.093
2.088
2.403
2.937
2.915
3.26
60
0.679
1.296
1.671
2.000
2.390
3.23
1.994
70
80
0.678
0.678
1.294
1.292
1.667
1.664
3.21
3.19
3.18
2.381
1.990
1.987
2.374
2.368
2.899
2.887
2.878
0.846
90
0.677
0.846
1.042
1.291
1.662
2.084
1.660
1.646
100
0.677
0.675
0.845
0.842
1.290
1.984
1.962
1.960
2.081
2.364
2.871
2.813
2.807
1.042
2.626
3.17
3.09
3.09
1.037
2.056
2.054
2.330
2.326
2.581
2.576
1000
1.282
1.282
0.674
0.842
1.036
1.645
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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