price of two bonds (Bond A and Bond B) are equal.  The broker does not know the population standard deviation of the two securities.  The following information outlines the information for each sample: Stock A                                  Stock B n1=8                                      n2=13 X1=$86                                  X2=$94 s1=$4                                    s2=$12 If you count on the population variances not being equal.  Test the broker's claim at the .01 level.  Also, test to see whether the population variances are equal or not equal at

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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Related questions
Topic Video
Question

A broker believes that the average price of two bonds (Bond A and Bond B) are equal.  The broker does not know the population standard deviation of the two securities.  The following information outlines the information for each sample:

Stock A                                  Stock B

n1=8                                      n2=13

X1=$86                                  X2=$94

s1=$4                                    s2=$12

If you count on the population variances not being equal.  Test the broker's claim at the .01 level.  Also, test to see whether the population variances are equal or not equal at the 0.05 level.

alues of t for Selected
df = 10
Probabilities
0.05
0.05
t=-1.8125
t= 1.8125
Probabilites (Or Areas Under t-Distribution Curve)
Conf. Level
One Tail
Two Tails
0.1
0.3
0.5
0.7
0.8
0.9
0.95
0.98
0.99
0.05
0.1
0,005
0.01
0.45
0.35
0.15
0.1
0.025
0.05
0.25
0.01
0.9
0.7
0.5
0.3
0.2
0.02
d.f.
Values of t
1.0000
0.8165
0.5095
63.6559
3.0777
1.8856
6.3137
1.9626
1.3862
1.2498
1.1896
1.1558
12.7062
4.3027
3.1824
0.1584
31.8210
0.4447
0.4242
6.9645
4.5407
3.7469
0.1421
2.9200
9.9250
0.7649
5.8408
1.6377
1.5332
2.3534
2.1318
0.1366
2.7765
2.5706
2.4469
4
0.1338
0.4142
0.7407
4.6041
0.1322
0.4082
0.7267
1.4759
2.0150
3.3649
4.0321
3.1427
2.9979
2.8965
2.8214
2.7638
2.7181
3.7074
3.4995
6.
0.4043
0.4015
0.7176
1.1342
1.9432
0.1311
0.1303
1.4398
1.8946
1.8595
1.8331
1.8125
7
0.7111
1.1192
1.4149
2.3646
0.7064
0.7027
1.3968
1.3830
1.3722
3.3554
0.1297
0.1293
8
0.3995
1.1081
2.3060
3.2498
3.1693
3.1058
3.0545
3.0123
1.0997
0.3979
0.3966
0.3956
9
2.2622
10
0.1289
0.6998
1.0931
2.2281
1.3634
1.3562
1.7959
1.7823
0.6974
1.0877
1.0832
11
0.1286
2.2010
0.3947
2.1788
2.1604
0.6955
2.6810
0.1283
0.1281
12
1.7709
0.6938
0.6924
0.6912
2.6503
2.6245
13
0.3940
1.0795
1.3502
1.7613
1.7531
1.7459
1.7396
1.7341
1.7291
1.7247
1.7207
0.3933
0.3928
0.3923
0.3919
2.9768
1.0763
1.0735
1.0711
1.0690
1.3450
2.1448
0.1280
0.1278
14
2.9467
2.9208
2.8982
15
1,3406
2.1315
2.6025
1,3368
1.3334
16
0.1277
0.6901
2.1199
2.5835
0.6892
0.6884
2.5669
2.5524
2.5395
17
0.1276
2,1098
1.0672
1.0655
1.0640
1.3304
2.1009
2.8784
18
19
0.1274
0.3915
0.1274
0.1273
1.3277
1.3253
2.0930
2.0860
2.8609
2.8453
0.3912
0.6876
2.5280
2.5176
0.6870
0.3909
0.3906
20
21
0.1272
0.6864
1.0627
1.3232
2.0796
2.8314
2.5083
2.4999
2.4922
0.3904
1.3212
1.7171
1.7139
2.0739
2.0687
2.0639
2.8188
0.6858
0.6853
0.6848
0.6844
22
0.1271
1.0614
2.8073
2.7970
1.0603
1.0593
1.0584
1.0575
1.0567
23
0.1271
0.3902
1.3195
1.3178
1.3163
1.7109
1.7081
1.7056
24
0.1270
0.3900
0.1269
2.4851
2.7874
0.3898
0.3896
25
2.0595
2.7787
2.7707
26
0.1269
0.6840
1.3150
2.0555
2.4786
1.7033
1.7011
27
0.1268
0.3894
0.6837
1.3137
2.0518
2.4727
1,3125
2.4671
2.4620
2.4573
2.0484
2.7633
0.6834
0.6830
28
0.1268
0.3893
1.0560
0.1268
0.1267
2.7564
2.7500
29
0.3892
1.0553
1.3114
1.6991
2.0452
1.3104
2.0423
0.6828
0.6807
30
0.3890
1.0547
1.6973
2.7045
2.0211
2.0086
2.0003
40
0.1265
0.3881
1.0500
1.3031
1.6839
2.4233
2.4033
2.3901
2.6778
2.6603
0.6794
1.0473
1.0455
1.2987
1.6759
1.6706
1.6669
1.6641
0.3875
0.3872
50
0.1263
1.2958
0.6786
0.6780
60
0.1262
2.3808
2.3739
2.3685
1.2938
1.9944
2.6479
1.0442
1.0432
70
0.1261
0.3869
1.2922
2.6387
0.3867
0.3866
80
0.1261
0.6776
1.9901
1.0424
1.0418
1.0386
1.0375
0.6772
1.2910
1.6620
1.9867
2.6316
0.1260
0.1260
90
1.2901
2.3642
2.6259
0.3864
0.3858
0.6770
1.6602
1.9840
100
250
0.1258
0.6755
1.2849
1.6510
1.9695
2.3414
2.5956
500
0.1257
0.3855
0.6750
1.2832
1.6479
1.9647
2.3338
2.5857
See Normal Distribution
Transcribed Image Text:alues of t for Selected df = 10 Probabilities 0.05 0.05 t=-1.8125 t= 1.8125 Probabilites (Or Areas Under t-Distribution Curve) Conf. Level One Tail Two Tails 0.1 0.3 0.5 0.7 0.8 0.9 0.95 0.98 0.99 0.05 0.1 0,005 0.01 0.45 0.35 0.15 0.1 0.025 0.05 0.25 0.01 0.9 0.7 0.5 0.3 0.2 0.02 d.f. Values of t 1.0000 0.8165 0.5095 63.6559 3.0777 1.8856 6.3137 1.9626 1.3862 1.2498 1.1896 1.1558 12.7062 4.3027 3.1824 0.1584 31.8210 0.4447 0.4242 6.9645 4.5407 3.7469 0.1421 2.9200 9.9250 0.7649 5.8408 1.6377 1.5332 2.3534 2.1318 0.1366 2.7765 2.5706 2.4469 4 0.1338 0.4142 0.7407 4.6041 0.1322 0.4082 0.7267 1.4759 2.0150 3.3649 4.0321 3.1427 2.9979 2.8965 2.8214 2.7638 2.7181 3.7074 3.4995 6. 0.4043 0.4015 0.7176 1.1342 1.9432 0.1311 0.1303 1.4398 1.8946 1.8595 1.8331 1.8125 7 0.7111 1.1192 1.4149 2.3646 0.7064 0.7027 1.3968 1.3830 1.3722 3.3554 0.1297 0.1293 8 0.3995 1.1081 2.3060 3.2498 3.1693 3.1058 3.0545 3.0123 1.0997 0.3979 0.3966 0.3956 9 2.2622 10 0.1289 0.6998 1.0931 2.2281 1.3634 1.3562 1.7959 1.7823 0.6974 1.0877 1.0832 11 0.1286 2.2010 0.3947 2.1788 2.1604 0.6955 2.6810 0.1283 0.1281 12 1.7709 0.6938 0.6924 0.6912 2.6503 2.6245 13 0.3940 1.0795 1.3502 1.7613 1.7531 1.7459 1.7396 1.7341 1.7291 1.7247 1.7207 0.3933 0.3928 0.3923 0.3919 2.9768 1.0763 1.0735 1.0711 1.0690 1.3450 2.1448 0.1280 0.1278 14 2.9467 2.9208 2.8982 15 1,3406 2.1315 2.6025 1,3368 1.3334 16 0.1277 0.6901 2.1199 2.5835 0.6892 0.6884 2.5669 2.5524 2.5395 17 0.1276 2,1098 1.0672 1.0655 1.0640 1.3304 2.1009 2.8784 18 19 0.1274 0.3915 0.1274 0.1273 1.3277 1.3253 2.0930 2.0860 2.8609 2.8453 0.3912 0.6876 2.5280 2.5176 0.6870 0.3909 0.3906 20 21 0.1272 0.6864 1.0627 1.3232 2.0796 2.8314 2.5083 2.4999 2.4922 0.3904 1.3212 1.7171 1.7139 2.0739 2.0687 2.0639 2.8188 0.6858 0.6853 0.6848 0.6844 22 0.1271 1.0614 2.8073 2.7970 1.0603 1.0593 1.0584 1.0575 1.0567 23 0.1271 0.3902 1.3195 1.3178 1.3163 1.7109 1.7081 1.7056 24 0.1270 0.3900 0.1269 2.4851 2.7874 0.3898 0.3896 25 2.0595 2.7787 2.7707 26 0.1269 0.6840 1.3150 2.0555 2.4786 1.7033 1.7011 27 0.1268 0.3894 0.6837 1.3137 2.0518 2.4727 1,3125 2.4671 2.4620 2.4573 2.0484 2.7633 0.6834 0.6830 28 0.1268 0.3893 1.0560 0.1268 0.1267 2.7564 2.7500 29 0.3892 1.0553 1.3114 1.6991 2.0452 1.3104 2.0423 0.6828 0.6807 30 0.3890 1.0547 1.6973 2.7045 2.0211 2.0086 2.0003 40 0.1265 0.3881 1.0500 1.3031 1.6839 2.4233 2.4033 2.3901 2.6778 2.6603 0.6794 1.0473 1.0455 1.2987 1.6759 1.6706 1.6669 1.6641 0.3875 0.3872 50 0.1263 1.2958 0.6786 0.6780 60 0.1262 2.3808 2.3739 2.3685 1.2938 1.9944 2.6479 1.0442 1.0432 70 0.1261 0.3869 1.2922 2.6387 0.3867 0.3866 80 0.1261 0.6776 1.9901 1.0424 1.0418 1.0386 1.0375 0.6772 1.2910 1.6620 1.9867 2.6316 0.1260 0.1260 90 1.2901 2.3642 2.6259 0.3864 0.3858 0.6770 1.6602 1.9840 100 250 0.1258 0.6755 1.2849 1.6510 1.9695 2.3414 2.5956 500 0.1257 0.3855 0.6750 1.2832 1.6479 1.9647 2.3338 2.5857 See Normal Distribution
Standard Normal
Distribution Table
0,3944
z= 1.25
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0160
0.0199
0.0239
0.0279
0.0319
0.0359
0.0000
0.0398
0.0
0.0040
0.0080
0.0120
0.0636
0.1026
0.0714
0.1103
0.1
0.0438
0.0478
0.0517
0.0557
0.0596
0.0675
0.0753
0.0948
0.1064
0.1141
0.0987
0.1368
0.2
0.0793
0.0832
0.0871
0.0910
0.1406
0.1443
0.1480
0.1517
0.1293
0.1664
0.1255
0.1331
0.1179
0.1554
0.3
0.1217
0.4
0.1591
0.1628
0.1700
0.1736
0.1772
0.1808
0.1844
0.1879
0.2224
0.2157
0.2486
0.2794
0.2190
0.2088
0.2422
0.5
0.1915
0.1950
0.1985
0.2019
0.2054
0.2123
0.2454·
0.2517
0.2549
0.2357
0.2673
0.6
0.2257
0.2291
0.2324
0.2389
0.7
0.2580
0.2611
0.2642
0.2704
0.2734
0.2764
0.2823
0.2852
0.3133
0.3389
0.8
0.2881
0.2910
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3315
0.3340
0.3365
0.3264
0.3508
0.9
0.3159
0.3186
0.3212
0.3238
0.3289
0.3621
0.3577
0.3790
0.3599
0.3554
0.3770
0.3461
0.3485
0.3531
0.3438
0.3665
1.0
0.3413
1.1
0.3643
0.3686
0.3708
0.3729
0.3749
0.3810
0.3830
12
0.3869
0.4049
0.3907
0.3925
0,3944
0.3962
0.3980
0.3997
0.4015
0.3849
0.3888
0.4177
0.4147
0.4292
0.4066
0.4082
0.4099
0.4115
0.4131
0.4162
0.4032
0.4192
1.3
0.4306
0.4429
0.4319
0.4279
0.4406
0.4265
0.4251
0.4382
1.4
0.4207
0.4222
0.4236
0.4418
0.4525
0.4441
0.4545
1.5
0.4332
0.4345
0.4357
0.4370
0.4394
0.4535
0.4625
*0.4495
0.4505
0.4515
0.4474
0.4573
0.4656
1.6
0.4452
0.4463
0.4484
0.4633
0.4599
0.4678
0.4616
0.4693
0.4756
0.4608
0.4591
0.4671
0.4582
0.4554
0.4641
0.4713
1.7
0.4564
0.4706
0.4767
0.4699
0.4686
:0.4750.
0.4803
1.8
0.4649
0.4664
0.4761
0.4738
0.4793
0.4744
0.4719
0.4778
0.4826
0.4732
0.4788
1.9
0.4726
0.4808
0.4812
0.4817
0.4798
0.4842
0.4772
0.4783
2.0
2.1
0.4857
0.4890
0.4854
0.4850
0.4884
0.4821
0.4830
0.4834
0.4838
0.4846
0.4887
0.4913
0.4875
0.4878
0.4881
0.4868
0.4898
2.2
0.4861
0.4864
0.4871
0.4901
0.4904
0.4906
0.4909
0.4911
0.4916
0.4896
0.4920
2.3
0.4893
0.4936
0.4952
0.4964
0.4932
0.4934
0.4931
0.4948
0.4925
0.4927
0.4929
0.4918
0.4938
0.4922
0.4941
0.4956
2.4
0.4951
0.4963
0.4946
0.4949
0.4943
0.4957
2.5
0.4940
0.4945
0.4955
0.4959
0.4960
0.4961
0.4962
0.4953
0.4965
0.4974
2.6
2.7
0.4966
0.4967
0.4968
0.4969
0.4970
0.4971
0.4972
0.4973
0.4974
2.8
0.4975
0.4976
0.4977
0.4977
0.4978
0.4979
0.4979
0.4980
0.4981
0.4986
0.4986
0.4984
0.4989
2.9
0.4981
0.4982
0.4982
0.4983
0.4984
0.4985
0.4985
3.0
0.4987
0.4987
0.4987
0.4988
0.4988
0.4989
0.4989
0.4990
0.4990
Transcribed Image Text:Standard Normal Distribution Table 0,3944 z= 1.25 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0000 0.0398 0.0 0.0040 0.0080 0.0120 0.0636 0.1026 0.0714 0.1103 0.1 0.0438 0.0478 0.0517 0.0557 0.0596 0.0675 0.0753 0.0948 0.1064 0.1141 0.0987 0.1368 0.2 0.0793 0.0832 0.0871 0.0910 0.1406 0.1443 0.1480 0.1517 0.1293 0.1664 0.1255 0.1331 0.1179 0.1554 0.3 0.1217 0.4 0.1591 0.1628 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.2224 0.2157 0.2486 0.2794 0.2190 0.2088 0.2422 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2123 0.2454· 0.2517 0.2549 0.2357 0.2673 0.6 0.2257 0.2291 0.2324 0.2389 0.7 0.2580 0.2611 0.2642 0.2704 0.2734 0.2764 0.2823 0.2852 0.3133 0.3389 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3315 0.3340 0.3365 0.3264 0.3508 0.9 0.3159 0.3186 0.3212 0.3238 0.3289 0.3621 0.3577 0.3790 0.3599 0.3554 0.3770 0.3461 0.3485 0.3531 0.3438 0.3665 1.0 0.3413 1.1 0.3643 0.3686 0.3708 0.3729 0.3749 0.3810 0.3830 12 0.3869 0.4049 0.3907 0.3925 0,3944 0.3962 0.3980 0.3997 0.4015 0.3849 0.3888 0.4177 0.4147 0.4292 0.4066 0.4082 0.4099 0.4115 0.4131 0.4162 0.4032 0.4192 1.3 0.4306 0.4429 0.4319 0.4279 0.4406 0.4265 0.4251 0.4382 1.4 0.4207 0.4222 0.4236 0.4418 0.4525 0.4441 0.4545 1.5 0.4332 0.4345 0.4357 0.4370 0.4394 0.4535 0.4625 *0.4495 0.4505 0.4515 0.4474 0.4573 0.4656 1.6 0.4452 0.4463 0.4484 0.4633 0.4599 0.4678 0.4616 0.4693 0.4756 0.4608 0.4591 0.4671 0.4582 0.4554 0.4641 0.4713 1.7 0.4564 0.4706 0.4767 0.4699 0.4686 :0.4750. 0.4803 1.8 0.4649 0.4664 0.4761 0.4738 0.4793 0.4744 0.4719 0.4778 0.4826 0.4732 0.4788 1.9 0.4726 0.4808 0.4812 0.4817 0.4798 0.4842 0.4772 0.4783 2.0 2.1 0.4857 0.4890 0.4854 0.4850 0.4884 0.4821 0.4830 0.4834 0.4838 0.4846 0.4887 0.4913 0.4875 0.4878 0.4881 0.4868 0.4898 2.2 0.4861 0.4864 0.4871 0.4901 0.4904 0.4906 0.4909 0.4911 0.4916 0.4896 0.4920 2.3 0.4893 0.4936 0.4952 0.4964 0.4932 0.4934 0.4931 0.4948 0.4925 0.4927 0.4929 0.4918 0.4938 0.4922 0.4941 0.4956 2.4 0.4951 0.4963 0.4946 0.4949 0.4943 0.4957 2.5 0.4940 0.4945 0.4955 0.4959 0.4960 0.4961 0.4962 0.4953 0.4965 0.4974 2.6 2.7 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974 2.8 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 0.4986 0.4986 0.4984 0.4989 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4985 0.4985 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4990 0.4990
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Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman