A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation s, is found to be 10. (a) Construct an 80% confidence interval about u if the sample size, n, is 15. (b) Construct an 80% confidence interval about u if the sample size, n, is 28. (c) Construct a 90% confidence interval about u if the sample size, n, is 15. (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 an 80% confidence interval about u if the sample size, n, is 15. Lower bound: 106.5 ; Upper bound: 113.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct an 80% confidence interval about u if the sample size, n, is 28. Lower bound: ; Upper bound: (Use ascending order. Round to one decimal place as needed.)

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Please answer parts B, C and D.

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 110, and the sample standard deviation,
s, is found to be 10.
(a) Construct an 80% confidence interval about u if the sample size, n, is 15.
(b) Construct an 80% confidence interval about u if the sample size, n, is 28.
(c) Construct a 90% confidence interval about u if the sample size, n, is 15.
(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 an 80% confidence interval about u if the sample size, n, is 15.
Lower bound: 106.5 ; Upper bound: 113.5
(Use ascending order. Round to one decimal place as needed.)
(b) Construct an 80% confidence interval about u if the sample size, n, is 28.
Lower bound:
; Upper bound:
(Use ascending order. Round to one decimal place as needed.)
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 110, and the sample standard deviation, s, is found to be 10. (a) Construct an 80% confidence interval about u if the sample size, n, is 15. (b) Construct an 80% confidence interval about u if the sample size, n, is 28. (c) Construct a 90% confidence interval about u if the sample size, n, is 15. (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 an 80% confidence interval about u if the sample size, n, is 15. Lower bound: 106.5 ; Upper bound: 113.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct an 80% confidence interval about u if the sample size, n, is 28. Lower bound: ; Upper bound: (Use ascending order. Round to one decimal place as needed.)
Table of t-Distribution Areas
-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
12.706
127.321
318.309
22.327
1
1.376
1.963
3.078
6.314
15.894
31.821
63.657
9.925
5.841
4.604
1.000
636.619
1.386
1.250
1.190
1.156
14.089
7.453
5.598
2.920
6.965
0.816
0.765
0.741
1.061
0.978
0.941
1.886
1.638
1.533
4.303
3.182
2.776
4.849
3.482
2.999
2.757
31.599
12.924
2.353
2.132
2.015
4.541
3.747
3.365
10.215
7.173
5.893
4
8.610
5
0.727
0.920
1.476
2.571
4.032
4.773
6.869
1.134
1.119
2.447
2.365
3.143
2.998
2.896
2.821
2.764
0.718
0.906
3.707
5.959
1.440
1.415
1.397
1.383
1.372
1.943
2.612
2.517
2.449
2.398
2.359
4.317
5.208
3.499
3.355
3.250
5.408
5.041
4.781
4.587
7
0.711
0.896
1.895
4.029
2.306
2.262
2.228
4.785
4.501
4.297
4.144
1.108
8
0.706 0.889
9
0.703
0.700
0.883
0.879
1.860
1.833
3.833
3.690
1.100
10
1.093
1.812
3.169
3.581
0.697
3.497
1.363
1.356
1.350
3.106
3.055
3.012
11
4.025
0.876
0.873
0.870
1.088
1.796
1.782
1.771
2.201
1.083
1.079
2.328
2.303
2.718
2.681
2.650
4.437
4.318
4.221
12
0.695
2.179
3.428
3.930
13
0.694
2.160
2.282
3.372
3.852
23
Transcribed Image Text:Table of t-Distribution Areas -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 12.706 127.321 318.309 22.327 1 1.376 1.963 3.078 6.314 15.894 31.821 63.657 9.925 5.841 4.604 1.000 636.619 1.386 1.250 1.190 1.156 14.089 7.453 5.598 2.920 6.965 0.816 0.765 0.741 1.061 0.978 0.941 1.886 1.638 1.533 4.303 3.182 2.776 4.849 3.482 2.999 2.757 31.599 12.924 2.353 2.132 2.015 4.541 3.747 3.365 10.215 7.173 5.893 4 8.610 5 0.727 0.920 1.476 2.571 4.032 4.773 6.869 1.134 1.119 2.447 2.365 3.143 2.998 2.896 2.821 2.764 0.718 0.906 3.707 5.959 1.440 1.415 1.397 1.383 1.372 1.943 2.612 2.517 2.449 2.398 2.359 4.317 5.208 3.499 3.355 3.250 5.408 5.041 4.781 4.587 7 0.711 0.896 1.895 4.029 2.306 2.262 2.228 4.785 4.501 4.297 4.144 1.108 8 0.706 0.889 9 0.703 0.700 0.883 0.879 1.860 1.833 3.833 3.690 1.100 10 1.093 1.812 3.169 3.581 0.697 3.497 1.363 1.356 1.350 3.106 3.055 3.012 11 4.025 0.876 0.873 0.870 1.088 1.796 1.782 1.771 2.201 1.083 1.079 2.328 2.303 2.718 2.681 2.650 4.437 4.318 4.221 12 0.695 2.179 3.428 3.930 13 0.694 2.160 2.282 3.372 3.852 23
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