A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 111, 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 17. (b) Construct a 90% confidence interval about u if the sample size, n, is 25. (c) Construct a 98% confidence interval about u if the sample size, n, is 17. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? 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 17. Lower bound: Upper bound: (Use ascending order. Round to one decimal place as needed.)
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 111, 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 17. (b) Construct a 90% confidence interval about u if the sample size, n, is 25. (c) Construct a 98% confidence interval about u if the sample size, n, is 17. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? 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 17. Lower bound: Upper bound: (Use ascending order. Round to one decimal place as needed.)
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Transcribed Image Text:A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 111, and the sample standard
deviation, s, is found to be 10.
(a) Construct a 90% confidence interval aboutu if the sample size, n, is 17.
(b) Construct a 90% confidence interval about u if the sample size, n, is 25.
(c) Construct a 98% confidence interval aboutu if the sample size, n, is 17.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
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 17.
Lower bound: Upper bound:
(Use ascending order. Round to one decimal place as needed.)
Transcribed Image Text:5
0.727
0.920
1.156 1.476 2.015
2.571
2.757
3.365
4.032
4.773
5.893
5.208
4.785
4.501
4.297
4.144
6.869
6 0.718
7.
6.
0.906
0.896
0.889
0.883
0.879
1.134
1.119
1.108
1.440
1.943
7 0.711
8 0.706
6.
2.447
2.365
2.306
2.262
2.228
2.612
2.517
2.449
2.398
2.359
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
5.959
5.408
5.041
4.781
4.587
1.415
1.895
1.397
1.860
1.383 1.833
1.372
0.703
1.100
Area in
10
0.700
1.093
1.812
right tail
11
12
13
0.697
0.695
0.694
0.692
0.691
0.876
0.873
0.870
0.868
0.866
1.088
1.083
1.079
1.076
1.074
1.363 1.796
1.356
1.782
1.350 1.771
1.345 1.761
1.341
2.201
2.179
2.160
2.145
2.131
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
2.947
3.497
3.428
3.372
3.326
3.286
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
4.140
4.073
14
15
1.753
Table VI
16
17
18
19
20
0.690
0.689
0.688
0.688
0.687
0.865
0.863
0.862
0.861
0.860
1.071
1.069
1.067
1.066
1.064
1.337
1.746
1.740
1.330 1.734
1.328
2.120
2.110
2.101
2.093
2.086
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
2.921
2.898
2.878
2.861
2.845
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.610
3.579
3.552
4.015
3.965
3.922
3.883
3.850
-Distribution
1.333
Area in Right Tail
1.729
1.325 1.725
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
1.000
0.816
3
21
22
23
24
25
0.686
0.686
0.685
0.685
0.859
0.858
0.858
0.857
0.856
1.063
1.061
1.060
1.059
1.058
1.323
1.321
1.319
1.318
1.316
1.721
1.717
1.714
2.080
2.074
2.069
2.064
2.060
2.189
2.183
2.177
2.172
2.167
2.518
2.508
2.500
2.492
2.485
2.831
2.819
2.807
2.797
2.787
3.135
3.119
3.104
3.091
3.078
3.527
3.505
3.485
3.467
3.450
3.819
3.792
3.768
3.745
3.725
1.376
1.963
3.078
1.886
1.638
1.533
1.476
6.314
2.920
2.353
2.132
2.015
12.706
4.303
3.182
2.776
2.571
15.894
4.849
3.482
2.999
2.757
31.821
6.965
4.541
3.747
3.365
63.657
9.925
5.841
4.604
4.032
127.321
14.089
7.453
5.598
4.773
318.309
22.327
10.215
7.173
5.893
636.619
31.599
12.924
8.610
6.869
1.061
1.386
0.765
0.741
0.727
0.978 1.250
1.711
1.708
4
0.941
1.190
0.920
1.156
0.684
0.684
26
27
28
29
30
0.856
0.855
0.855
0.854
0.854
1.058
1.057
1.056
1.055
1.055
1.315
1.314
1.313
1.311
1.310
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
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
6.
7.
0.718
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
2.612
2.517
0.711
0.706
0.703
2.449
2.398
2.359
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
5.208 . 5.959
4.785
4.501
4.297
4.144
5.408
5.041
4.781
4.587
0.684
0.683
0.683
0.683
2.763
2.756
2.750
6.
0.700
10
2.144
2.141
2.138
11
31
32
0.697
0.695
0.694
0.692
0.691
0.876
0.873
0.870
0.868
0.866
2.201
2.179
2.160
2.145
2.131
0.682
0.682
0.682
0.682
0.682
0.853
0.853
0.853
0.852
0.852
3.633
3.622
3.611
3.601
3.591
1.054
1.054
1.309
1.309
1.308
1.307
1.696
12
13
14
15
1.088
1.083
1.079
1.076
1.074
1.363
1.356
1.350
1.345
1.796
1.782
1.771
1.761
1.753
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
2.947
3.497
3.428
3.372
3.326
3.286
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
4.140
4.073
2.040
2.037
2.035
2.032
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
3.375
3.365
3.356
3.348
3.340
1.694
33
34
35
1.053
1.052
1.052
1.692
1.691
1.690
2.136
1.341
1.306
2.030
2.133
16
17
18
19
20
0.690
0.689
0.688
0.688
0.687
0.865
0.863
0.862
0.861
0.860
1.071
1.069
1.067
1.337
1.746
2.120
2.110
2.101
2.093
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
3.252
3.222
3.197
3.174
3.153
36
37
0.681
0.681
2.921
2.898
2.878
2.861
2.845
3.686
3.646
3.610
3.579
3.552
4.015
3.965
3.922
3.883
3.850
0.852
0.851
0.851
0.851
0.851
1.052
1.051
1.051
1.050
1.050
1.306
1.305
1.304
1.304
1.303
1.688
1.687
1.686
1.685
1.684
2.028
2.026
2.024
2.023
2.021
2.131
2.129
2.127
2.125
2.123
2.434
2.431
2.429
2.426
2.423
2.719
2.715
2.712
2.708
2.704
2.990
2.985
2.980
2.976
2.971
3.333
3.326
3.319
3.313
3.307
3.582
3.574
3.566
3.558
3.551
1.333
1.740
1.734
1.328 1.729
1.325
1.330
38
0.681
1.066
1.064
39
0.681
0.681
1.725
2.086
40
21
22
0.686
0.859
0.858
0.858
0.857
0.856
1.063
1.061
1.060
1.059
1.323
1.721
2.080
2.074
2.069
2.064
2.060
2.189
2.183
2.177
2.172
2.518
2.831
2.819
2.807
2.797
2.787
3.135
3,119
3.104
3.091
3.078
3.527
3.505
3,485
3.467
3.450
3.819
3.792
3.768
3.745
3.725
2.937
2.915
2.899
2.887
2.878
3.261
3.232
3.211
3.195
3.183
3.496
3.460
3.435
3.416
3.402
50
0.679
0.679
0.678
0.678
0.677
0.849
0.848
0.847
0.846
0.846
1.047
1.299
1.296
1.294
1.292
1.291
1.676
1.671
2.009
2.000
2.109
2.099
2.403
2.390
2.381
2.374
2.368
2.678
2.660
0.686
0.685
0.685
0.684
1.321
1.717
1.319 1.714
1.318 1.711
2.508
2.500
2.492
2.485
60
1.045
23
24
25
70
80
90
1.044
1.043
1.042
1.667
1.664
1.662
1.994
1.990
1.987
2.093
2.088
2.084
2.648
2.639
2.632
1.058
1.316
1.708
2.167
26
27
28
29
0.684
0.856
0.855
0.855
0.854
0.854
1.058
1.057
1.056
1.055
1.315
1.314
1.313
1.311
1.310
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
2.479
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
1.660
1.290
1.646
1.282
1.282 1.645
2.626
2.581
2.576
2.871
100
1000
0.677
0.675
0.674
0.845
0.842
0.842
1.042
1.037
1.036
1.984
1.962
1.960
2.081
2.056
2.054
2.364
2.330
2326
3.174
3.098
3.090
3.390
3.300
3.291
0.684
0.683
0.683
0.683
2.473
2.467
2.462
2.813
2.807
30
1.055
2.147
2.457
3.646
0.25
0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
0.0005
JP
31
32
0.682
0.682
0.853
0.853
1.054
1.054
1.309
1.309
2.144
2.141
2.453
2.449
1.696
2.040
2.037
2.744
2.738
3.022
3.375
3.365
3.633
3.622
1.694
3.015
Area in Right Tail
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