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 4.5. 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?
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 4.5. 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
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Question
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Transcribed Image Text: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 4.5.
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?
A. The margin of error does not change.
B. The margin of error increases.
O c. The margin of error decreases.
(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.
B. The margin of error increases.
O 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 must come from a population that is normally distributed and the sample size must be large.
O B. The sample size must be large and the sample should not have any outliers.
C. The sample data must come from a population that is normally distributed with no outliers.
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
127.321
1.000
0.816
3
1.963
1.386
3.078
1.886
1.638
1.533
1.476
6.314
2.920
2.353
2.132
2.015
12.706
15.894
4.849
31.821
318.309
22.327
636.619
31.599
12.924
8.610
6.869
1.376
63.657
4.303
3.182
2.776
2.571
9.925
5,841
4.604
2
1.061
0.978
0.941
0.920
6.965
14.089
7.453
5.598
4.773
0.765
0.741
3.482
2.999
2.757
1.250
4,541
1.190
1.156
3.747
3.365
10.215
7.173
5.893
0.727
4.032
1.134
1.119
1.440
1.415
1.397
1.383
1.372
2.447
2.365
2.306
2.262
2.228
0.906
0.896
5.959
5.408
1.943
1.895
1.860
1.833
1.812
2.612
2.517
3.143
2.998
2.896
2.821
2.764
3.707
3.499
3.355
3.250
3.169
4.317
4.029
3.833
3.690
3.581
0.718
0.711
5.208
4.785
7
0.889
0.883
8
0.706
1.108
2.449
4.501
4.297
5.041
0.703
1.100
1.093
9
2.398
4.781
10
0.700
0.879
2.359
4.144
4.587
0.876
0.873
1.363
1.356
1.350
1.345
1.341
2.201
2.179
11
12
13
2.328
2.303
2.282
2.264
2.249
2.718
2.681
2.650
2.624
2.602
3.106
3.055
3.012
2.977
3.497
3.428
3.372
3.326
3.286
4.025
3.930
3.852
3.787
3.733
0.697
4.437
4.318
4.221
4.140
4.073
1.088
1.796
1.083
1.782
1.771
1.761
1.753
0.695
0.694
0.870
1.079
2.160
0.692
0.691
0.868
0.866
2.145
2.131
14
1.076
15
1.074
2.947
2.120
2.110
2.101
2.093
2.086
3.252
3.222
3.197
3.174
3.153
16
0.690
0.865
1.071
1.337
1.333
1.330
1.328
1.325
1.746
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
2.921
3.686
0.689
0.688
0.688
0.687
1.069
1.067
1.066
1.064
1.740
1.734
1.729
1.725
2,898
2.878
2.861
2.845
3.646
3.610
3.579
3.552
4.015
3.965
3.922
3.883
3.850
17
0.863
0.862
0.861
0.860
18
19
20
0.686
0.859
0.858
0.858
0.857
0.856
1.063
1.061
1.060
1.059
1.058
1.721
1.717
1.714
1.711
1.708
2.518
2.508
2.500
2.492
2.485
2.831
2.819
2.807
2.797
2.787
3.135
3.119
3.527
3.505
3.485
3.467
3.450
21
1.323
2.080
2.189
2.183
2.177
2.172
2.167
3.819
3.792
3.768
3.745
3.725
1.321
2.074
2.069
2.064
2.060
22
0.686
23
0.685
0.685
0.684
1.319
1.318
1.316
3.104
3.091
24
25
3.078
26
27
28
29
30
0.684
0.684
0.683
0.683
0.683
0.856
0.855
0.855
0.854
0.854
1.058
1.057
1.056
1.055
1.055
1.706
1.703
1.701
1.699
1.697
2.056
2.052
2.048
2.045
2.042
2.162
2.158
2.154
2.150
2.147
2.479
2.473
2.467
2.462
2.457
2.779
2.771
2.763
2.756
2.750
3.067
3.057
3.047
3.038
3.030
3.435
3.421
3.408
3.396
3.385
3.707
3.690
3.674
3.659
3.646
1.315
1.314
1.313
1.311
1.310
0.682
0.682
0.682
0.853
0.853
1.054
1.054
1.053
1.052
1.052
1.696
1.694
1.692
1.691
1.690
2.040
2.037
2.035
2.032
2.030
2.453
2.449
31
32
33
34
35
0.853
0.852
0.852
1.309
1.309
1.308
1.307
1.306
2.144
2.141
2.138
2.136
2.133
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
3.375
3.365
3.356
3.348
3.340
3.633
3.622
3.611
0.682
3.601
0.682
3.591
0.852
0.851
0.851
0.851
0.851
1.052
1.051
1.051
1.050
1.050
1.688
1.687
1.686
1.685
1.684
2.434
2.431
2.429
3.333
3.326
3.319
3.313
3.307
36
0.681
0.681
0.681
0.681
0.681
1.306
1.305
1.304
1.304
1.303
2.028
2.026
2.024
2.023
2.021
2.131
2.129
2.127
2.719
2.715
2.712
2.708
2.704
2.990
3.582
37
38
39
2.985
2.980
2.976
2.971
3.574
3.566
2.125
2.123
2.426
3.558
40
2.423
3.551
0.679
0.679
1.047
1.045
1.044
1.043
2.009
2.000
1.994
1.990
2.678
2.660
2.648
2.639
2.109
2.099
2.937
2.915
3.261
3.232
50
0.849
0.848
0.847
0.846
1.299
1.296
1.676
1.671
1.667
1.664
2.403
2.390
2.381
2.374
3.496
3.460
3.435
3.416
60
2.093
2.088
3.211
3.195
70
0.678
0.678
1.294
1.292
2.899
80
2.887
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