A group of researchers developed a 95% z confidence interval for the mean body mass index (BMI) of women aged 20 to 29 years, based on a national random sample of 657 such women. They assumed that the population standard deviation was known to be o = 7.5. In fact, the sample data had mean BMI x = 26.9 and standard deviation s = 7.67. What is the 95% t confidence interval for the mean BMI of all young women? (Round your answers to three decimal places.) X to | t distribution critical values Confidence leel C Degrees of freedom 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1.376 1.061 0.978 1.963 1.386 1.250 3.078 1.886 6.314 2.920 2.353 2.132 2.015 12.71 4.303 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 63.66 9.925 127.3 14.09 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 1.000 0.816 318.3 22.33 15.89 636.6 31.60 4.849 3.482 5.841 4.604 4.032 3.707 3.499 3 0.765 1.638 3.182 10.21 12.92 1.190 1.156 1.533 1.476 1.440 1.943 1.415 1.895 1.397 0.741 0.727 0.941 0.920 7.173 5.893 2.776 2.999 2.757 2.612 2.517 2.449 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 4 2.571 5.208 4.785 4.501 4.297 4.144 4.025 3.930 0.711 0.706 0.718 0.906 1.134 0.896 0.889 1.119 1.106 2.447 2.365 7 1.860 2.306 3.355 0.703 0.700 2.262 2.228 2.201 0.883 1.100 1.383 1.372 1.363 1.356 1.833 2.398 2.821 3.250 10 0.879 1.093 1.812 2.359 2.764 3.169 0.876 0.695 0.873 1.083 1.796 1.782 3.497 3.428 1.068 11 12 2.328 2.303 2.718 2.681 2.650 3.106 3.055 0.697 2.179 0.694 0.870 1.079 0.868 1.076 1.074 1.071 1.069 13 1.350 1.771 2.160 2.282 3.012 3.372 3.852 14 15 0.692 0.691 1.761 1.753 2.624 2.602 3.787 3.733 1.345 1.341 1.337 1.333 2.145 2.131 2.120 2.110 2.264 2.249 2.235 2.224 2.214 2.977 2.947 2.921 2.898 3.326 3.286 0.866 16 17 0.690 0.689 0.865 0.863 1.746 1.740 1.734 2.583 2.567 2.552 3.252 3.222 3.197 3.686 3.646 3.611 18 0.688 0.862 1.067 1.330 2.101 2.878 1.066 19 20 2.093 2.086 3.174 3.153 3.579 3.552 3.527 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.856 0.684 0.855 0.683 0.683 0.683 0.861 0.860 1.064 1.325 0.859 0.858 0.858 1.328 1.729 1.725 1.721 1.717 2.205 2.197 2.539 2.528 2.518 2.861 2.845 2.831 2.819 2.807 2.797 2.787 3.883 3.850 2.080 2.074 2.069 2.064 2.060 21 1.063 1.323 2.189 3.135 3.819 1.061 1.060 1.059 1.058 1.058 2.183 2.177 2.172 2.167 2.162 1.321 1319 2.508 2.500 3.792 3.768 3.119 3.104 3.091 3.078 3.505 3.485 3.467 3.450 3.435 3.421 3.408 22 23 0.857 0.856 1318 1.316 1.315 1.714 1.711 1.708 2.492 2.485 2.479 24 25 3.745 3.725 3.707 3.690 3.674 2.056 2.779 2.771 2.763 26 1.706 3.067 27 28 1.057 0.855 1.056 1.314 1313 1.055 1.311 1.703 1.701 1.699 2.158 2.154 2.150 2.052 2.473 2.467 2.462 2.457 2.423 2.403 2.390 2.048 2.045 2.042 3.057 3.047 3.038 0.854 0.854 0.851 0.849 0.848 1.045 1.296 1.671 0.846 29 30 3.396 3.385 2.756 3.659 2.147 2.123 2.109 2.099 2.750 2.704 2.678 2.660 2.639 2.626 2.581 1.055 1.310 1.697 3.030 3.646 3.551 40 50 60 1.050 1.303 1.684 1.047 1.299 2.971 2.937 2.915 0.681 2.021 3.307 0.679 1.676 2.009 3.261 3.496 3.460 3.416 3.390 0.679 2.000 3.232 0.678 0.677 0.845 0.675 0.842 1.043 1.042 1.037 1.036 1.664 1.660 1.646 1.645 1.990 1.984 1.962 1.960 80 100 1.292 1.290 1.282 2.088 2.081 2.056 2.054 2.374 2.364 2.330 2.887 2.871 3.195 3.174 3.098 1000 2.813 3.300 ** 0.674 0.841 1.282 2.326 2.576 2.807 3.091 3.291 One-sided P .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 Two-sided P .50 40 30 20 .10 05 .04 .02 .01 .005 .002 .001
A group of researchers developed a 95% z confidence interval for the mean body mass index (BMI) of women aged 20 to 29 years, based on a national random sample of 657 such women. They assumed that the population standard deviation was known to be o = 7.5. In fact, the sample data had mean BMI x = 26.9 and standard deviation s = 7.67. What is the 95% t confidence interval for the mean BMI of all young women? (Round your answers to three decimal places.) X to | t distribution critical values Confidence leel C Degrees of freedom 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1.376 1.061 0.978 1.963 1.386 1.250 3.078 1.886 6.314 2.920 2.353 2.132 2.015 12.71 4.303 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 63.66 9.925 127.3 14.09 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 1.000 0.816 318.3 22.33 15.89 636.6 31.60 4.849 3.482 5.841 4.604 4.032 3.707 3.499 3 0.765 1.638 3.182 10.21 12.92 1.190 1.156 1.533 1.476 1.440 1.943 1.415 1.895 1.397 0.741 0.727 0.941 0.920 7.173 5.893 2.776 2.999 2.757 2.612 2.517 2.449 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 4 2.571 5.208 4.785 4.501 4.297 4.144 4.025 3.930 0.711 0.706 0.718 0.906 1.134 0.896 0.889 1.119 1.106 2.447 2.365 7 1.860 2.306 3.355 0.703 0.700 2.262 2.228 2.201 0.883 1.100 1.383 1.372 1.363 1.356 1.833 2.398 2.821 3.250 10 0.879 1.093 1.812 2.359 2.764 3.169 0.876 0.695 0.873 1.083 1.796 1.782 3.497 3.428 1.068 11 12 2.328 2.303 2.718 2.681 2.650 3.106 3.055 0.697 2.179 0.694 0.870 1.079 0.868 1.076 1.074 1.071 1.069 13 1.350 1.771 2.160 2.282 3.012 3.372 3.852 14 15 0.692 0.691 1.761 1.753 2.624 2.602 3.787 3.733 1.345 1.341 1.337 1.333 2.145 2.131 2.120 2.110 2.264 2.249 2.235 2.224 2.214 2.977 2.947 2.921 2.898 3.326 3.286 0.866 16 17 0.690 0.689 0.865 0.863 1.746 1.740 1.734 2.583 2.567 2.552 3.252 3.222 3.197 3.686 3.646 3.611 18 0.688 0.862 1.067 1.330 2.101 2.878 1.066 19 20 2.093 2.086 3.174 3.153 3.579 3.552 3.527 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.856 0.684 0.855 0.683 0.683 0.683 0.861 0.860 1.064 1.325 0.859 0.858 0.858 1.328 1.729 1.725 1.721 1.717 2.205 2.197 2.539 2.528 2.518 2.861 2.845 2.831 2.819 2.807 2.797 2.787 3.883 3.850 2.080 2.074 2.069 2.064 2.060 21 1.063 1.323 2.189 3.135 3.819 1.061 1.060 1.059 1.058 1.058 2.183 2.177 2.172 2.167 2.162 1.321 1319 2.508 2.500 3.792 3.768 3.119 3.104 3.091 3.078 3.505 3.485 3.467 3.450 3.435 3.421 3.408 22 23 0.857 0.856 1318 1.316 1.315 1.714 1.711 1.708 2.492 2.485 2.479 24 25 3.745 3.725 3.707 3.690 3.674 2.056 2.779 2.771 2.763 26 1.706 3.067 27 28 1.057 0.855 1.056 1.314 1313 1.055 1.311 1.703 1.701 1.699 2.158 2.154 2.150 2.052 2.473 2.467 2.462 2.457 2.423 2.403 2.390 2.048 2.045 2.042 3.057 3.047 3.038 0.854 0.854 0.851 0.849 0.848 1.045 1.296 1.671 0.846 29 30 3.396 3.385 2.756 3.659 2.147 2.123 2.109 2.099 2.750 2.704 2.678 2.660 2.639 2.626 2.581 1.055 1.310 1.697 3.030 3.646 3.551 40 50 60 1.050 1.303 1.684 1.047 1.299 2.971 2.937 2.915 0.681 2.021 3.307 0.679 1.676 2.009 3.261 3.496 3.460 3.416 3.390 0.679 2.000 3.232 0.678 0.677 0.845 0.675 0.842 1.043 1.042 1.037 1.036 1.664 1.660 1.646 1.645 1.990 1.984 1.962 1.960 80 100 1.292 1.290 1.282 2.088 2.081 2.056 2.054 2.374 2.364 2.330 2.887 2.871 3.195 3.174 3.098 1000 2.813 3.300 ** 0.674 0.841 1.282 2.326 2.576 2.807 3.091 3.291 One-sided P .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 Two-sided P .50 40 30 20 .10 05 .04 .02 .01 .005 .002 .001
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
Transcribed Image Text:A group of researchers developed a 95% z confidence interval for the mean body mass index (BMI) of women aged 20 to 29 years, based on a
national random sample of 657 such women. They assumed that the population standard deviation was known to be o = 7.5. In fact, the sample
data had mean BMI x = 26.9 and standard deviation s = 7.67. What is the 95% t confidence interval for the mean BMI of all young women? (Round
your answers to three decimal places.)
X to |
Transcribed Image Text:t distribution critical values
Confidence leel C
Degrees
of freedom
50%
60%
70%
80%
90%
95%
96%
98%
99%
99.5%
99.8%
99.9%
1.376
1.061
0.978
1.963
1.386
1.250
3.078
1.886
6.314
2.920
2.353
2.132
2.015
12.71
4.303
31.82
6.965
4.541
3.747
3.365
3.143
2.998
2.896
63.66
9.925
127.3
14.09
7.453
5.598
4.773
4.317
4.029
3.833
3.690
3.581
1.000
0.816
318.3
22.33
15.89
636.6
31.60
4.849
3.482
5.841
4.604
4.032
3.707
3.499
3
0.765
1.638
3.182
10.21
12.92
1.190
1.156
1.533
1.476
1.440 1.943
1.415 1.895
1.397
0.741
0.727
0.941
0.920
7.173
5.893
2.776
2.999
2.757
2.612
2.517
2.449
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
4
2.571
5.208
4.785
4.501
4.297
4.144
4.025
3.930
0.711
0.706
0.718 0.906 1.134
0.896
0.889
1.119
1.106
2.447
2.365
7
1.860
2.306
3.355
0.703
0.700
2.262
2.228
2.201
0.883 1.100
1.383
1.372
1.363
1.356
1.833
2.398
2.821
3.250
10
0.879 1.093
1.812
2.359
2.764
3.169
0.876
0.695 0.873 1.083
1.796
1.782
3.497
3.428
1.068
11
12
2.328
2.303
2.718
2.681
2.650
3.106
3.055
0.697
2.179
0.694 0.870 1.079
0.868 1.076
1.074
1.071
1.069
13
1.350
1.771
2.160
2.282
3.012
3.372
3.852
14
15
0.692
0.691
1.761
1.753
2.624
2.602
3.787
3.733
1.345
1.341
1.337
1.333
2.145
2.131
2.120
2.110
2.264
2.249
2.235
2.224
2.214
2.977
2.947
2.921
2.898
3.326
3.286
0.866
16
17
0.690
0.689
0.865
0.863
1.746
1.740
1.734
2.583
2.567
2.552
3.252
3.222
3.197
3.686
3.646
3.611
18
0.688
0.862
1.067
1.330
2.101
2.878
1.066
19
20
2.093
2.086
3.174
3.153
3.579
3.552
3.527
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684 0.856
0.684 0.855
0.683
0.683
0.683
0.861
0.860 1.064 1.325
0.859
0.858
0.858
1.328
1.729
1.725
1.721
1.717
2.205
2.197
2.539
2.528
2.518
2.861
2.845
2.831
2.819
2.807
2.797
2.787
3.883
3.850
2.080
2.074
2.069
2.064
2.060
21
1.063
1.323
2.189
3.135
3.819
1.061
1.060
1.059
1.058
1.058
2.183
2.177
2.172
2.167
2.162
1.321
1319
2.508
2.500
3.792
3.768
3.119
3.104
3.091
3.078
3.505
3.485
3.467
3.450
3.435
3.421
3.408
22
23
0.857
0.856
1318
1.316
1.315
1.714
1.711
1.708
2.492
2.485
2.479
24
25
3.745
3.725
3.707
3.690
3.674
2.056
2.779
2.771
2.763
26
1.706
3.067
27
28
1.057
0.855 1.056
1.314
1313
1.055 1.311
1.703
1.701
1.699
2.158
2.154
2.150
2.052
2.473
2.467
2.462
2.457
2.423
2.403
2.390
2.048
2.045
2.042
3.057
3.047
3.038
0.854
0.854
0.851
0.849
0.848 1.045 1.296 1.671
0.846
29
30
3.396
3.385
2.756
3.659
2.147
2.123
2.109
2.099
2.750
2.704
2.678
2.660
2.639
2.626
2.581
1.055 1.310 1.697
3.030
3.646
3.551
40
50
60
1.050 1.303 1.684
1.047 1.299
2.971
2.937
2.915
0.681
2.021
3.307
0.679
1.676
2.009
3.261
3.496
3.460
3.416
3.390
0.679
2.000
3.232
0.678
0.677 0.845
0.675 0.842
1.043
1.042
1.037
1.036
1.664
1.660
1.646
1.645
1.990
1.984
1.962
1.960
80
100
1.292
1.290
1.282
2.088
2.081
2.056
2.054
2.374
2.364
2.330
2.887
2.871
3.195
3.174
3.098
1000
2.813
3.300
**
0.674
0.841
1.282
2.326
2.576
2.807
3.091
3.291
One-sided P
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.001
.0005
Two-sided P
.50
40
30
20
.10
05
.04
.02
.01
.005
.002
.001
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman