(a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: (Use ascending order. Round to two decimal places as needed.) Upper bound: (b) Construct a 95% confidence interval about u if the sample size, n, is 51. 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?
(a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: (Use ascending order. Round to two decimal places as needed.) Upper bound: (b) Construct a 95% confidence interval about u if the sample size, n, is 51. 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
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Question
10
Transcribed Image Text:A simple random sample of size n is drawn. The sample mean, x, is found to be 19.3, and the sample standard deviation, s, is found to be 4.1.
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 51.
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?
A. The margin of error does not change.
B. The margin of error decreases.
C. The margin of error increases.
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
1.963
1.386
1.376
1.061
0.978
12.706
4.303
3.182
2.776
2.571
127.321
14.089
7.453
5.598
4.773
1
3.078
6.314
2.920
15.894
4.849
31.821
6.965
4.541
3.747
3.365
63.657
318.309
22.327
1.000
0.816
3
636.619
31.599
12.924
8.610
9.925
5.841
2
1.250
1.190
1.156
1.886
1.638
1.533
1.476
2.353
2.132
2.015
3.482
2.999
2.757
10.215
7.173
5.893
0.765
4
0.741
0.727
0.941
0.920
4.604
4.032
6.869
0.906
0.896
0.889
0.883
0.879
1.134
1.119
1.108
1.100
1.093
1.440
1.415
1.397
1.383
1.372
1.943
1.895
1.860
1.833
1.812
2.447
2.365
2.306
2.262
2.228
3.143
2.998
2.896
2.821
2.764
3.707
3.499
3.355
3.250
3.169
5.208
4.785
4.501
4.297
4.144
6.
0.718
0.711
8
2.612
2.517
2.449
2.398
2.359
4.317
4.029
3.833
3.690
3.581
5.959
7
5.408
5.041
4.781
4.587
0.706
0.703
10
0.700
1.796
1.782
3.497
3.428
3.372
3.326
3.286
2.201
2.179
4.025
3.930
3.852
3.787
11
12
0.697
1.088
1.363
1.356
0.876
2.328
2.718
3.106
4.437
1.083
1.079
1.076
1.074
3.055
3.012
2.303
2.282
2.264
2.249
2.681
2.650
0.695
0.694
0.692
0.691
0.873
4.318
0.870
0.868
1.350
1.345
1.341
1.771
1.761
1.753
2.160
2.145
2.131
13
4.221
4.140
4.073
14
2.624
2.977
15
0.866
2.602
2.947
3.733
2.235
2.224
2.214
3.686
3.646
3.610
3.579
3.552
16
0.865
0.690
0.689
1.071
1.337
1.746
1.740
1.734
2.120
2.110
2.101
2.583
2.567
2.552
2.539
2.528
2.921
2.898
2.878
3.252
4.015
1.333
1.330
3.222
3.197
3.174
3.153
3.965
3.922
3.883
0.863
0.862
17
1.069
18
0.688
1.067
0.688
0.687
0.861
0.860
1.066
1.064
1.328
1.325
2.093
2.086
19
1.729
2.205
2.197
2.861
20
1.725
2.845
3.850
3.135
3.119
3.104
3.091
3.078
3.819
3.792
3.768
3.745
3.725
0.686
0.686
0.859
0.858
0.858
0.857
0.856
1.323
1.321
1.721
1.717
3.527
3.505
3.485
3.467
3.450
21
1.063
1.061
1.060
1.059
1.058
2.080
2.074
2.189
2.518
2.831
2.508
2.500
2.492
2.485
2.183
2.819
2.807
2.797
22
23
0.685
0.685
0.684
1.319
1.318
1.714
1.711
2.069
2.177
2.064
2.060
24
2.172
25
1.316
1.708
2.167
2.787
1.058
1.057
1.056
1.315
1.314
1.313
2.779
2.771
2.763
2.756
26
0.856
0.855
0.855
0.854
0.854
1.706
2.056
2.052
2.048
2.045
2.042
2.162
2.158
2.154
2.479
3.067
3.057
3.047
3.038
3.435
3.421
0.684
3.707
0.684
0.683
0.683
0.683
1.703
1.701
1.699
1.310 1.697
3.690
3.674
27
28
29
30
2.473
2.467
2.462
2.457
3.408
3.396
3.385
1.055
1.055
2.150
2.147
3.659
3.646
1.311
2.750
3.030
1.309
1.309
1.308
1.307
1.306
1.696
1.694
1.692
1.691
1.690
2.040
2.037
2.035
2.032
2.453
2.449
2.445
2.441
3.375
3.365
3.356
3.348
3.340
31
32
0.682
0.682
0.682
0.682
0.682
0.853
0.853
0.853
0.852
0.852
1.054
2.144
2.744
3.022
1.054
1.053
1.052
1.052
2.141
2.138
2.136
2.133
3.633
3.622
3.611
3.601
3.591
2.738
2.733
3.015
3.008
3.002
2.996
33
34
2.728
35
2.030
2.438
2.724
0.681
0.681
0.852
0.851
0.851
1.306
1.305
1.688
1.687
2.028
2.026
2.024
2.131
2.129
2.127
2.990
2.985
2.980
2.434
36
37
38
2.719
2.715
2.712
3.333
3.326
3.319
3.582
3.574
3.566
1.052
1.051
1.051
2.431
2.429
0.681
1.304
1.686
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