For a random sample of size n 100 from a normally distributed population has a sample 1. mean of 20.85 and a sample standard deviation ofs = 13.41. Find a: %3D a) 95% confidence interval for the population mean u b) 99% confidence interval for the population mean u Table II Normal Curve Areas .03 .02 .04 .06 .01 .05 .00 .07 .08 .09 .0239 .0636 .1026 .1406 .1772 .2123 .0120 .0160 .0557 .0948 .0080 0199 .0596 .0987 .0000 .0398 .0793 .1179 .0040 .0438 .0832 .1217 .1591 .1950 .0279 67వ .1064 .0359 .0753 .1141 .1517 .1879 2224 .0319 .0714 .1103 0517 .0478 .0871 .0910 .1331 .1700 2054 .1480 .1844 2190 .1255 .1628 .1985 .1293 .1664 2019 .1443 .1808 2157 .1368 .1736 2088 .1554 .1915 2549 2852 3133 3389 3621 2486 2517 2823 3106 3365 3599 2324 2257 2291 2389 2422 .2734 3023 3289 3531 .2454 2357 2794 3078 3340 3577 .2580 2881 3159 3413 2764 3051 3315 3554 2611 2910 3186 3438 .2704 2995 3264 3508 2642 2939 3212 2673 2967 3238 3485 3461 1.0 3830 4015 3790 3810 3708 3907 4082 4236 4370 .3729 .3925 3686 3749 .3770 3665 3643 1.1 3997 4162 4306 .4429 3980 3962 4131 4279 4406 3849 4032 3888 4066 4222 4357 3944 3869 4049 4207 4345 1.2 1.3 4177 .4319 4441 4147 4292 4418 4099 4251 4382 4115 4265 4394 A192 4332 1.4 1.5 4545 4633 4706 .4767 4817 4525 .4616 4693 .4535 4625 4699 4761 4812 4495 4591 4671 4515 4505 4474 4573 4656 A726 4783 4484 4463 4452 1.6 4608 A686 4599 4678 4744 4798 A582 A664 4732 4788 4554 4641 4713 4772 4564 4649 4719 4778 1.7 1.8 1.9 2.0 .4756 4808 4750 4738 4803 4793 4857 4890 4916 4936 4952 4846 4881 4850 4884 4854 4842 4878 4906 4929 4946 4834 4871 4901 4925 4943 4838 4826 4864 4896 4920 4940 4830 4821 2.1 4887 4913 4934 4951 4875 4904 4927 4945 4868 4898 4922 4941 4861 4893 4918 4938 2.2 2.3 2.4 2.5 4909 4931 4948 .4911 .4932 4949 4964 4963 4973 4980 4986 4990 4960 4961 4971 4979 4985 4959 .4962 4957 4956 4967 4976 4982 4987 4955 4966 4975 4982 4987 4953 A965 4974 4981 4987 2.6 2.7 2.8 2.9 3.0 4974 4981 4986 4969 4977 .4984 .4988 4972 4979 4985 4989 4970 4978 4984 4989 4968 4977 4983 4988 శ990 .4989 Source: Abridged from Table 1 of A.Hald, Stutistical Tables and Formulas (New York: Wiley). 1952.

For a random sample of size n 100 from a normally distributed population has a sample 1. mean of 20.85 and a sample standard deviation ofs = 13.41. Find a: %3D a) 95% confidence interval for the population mean u b) 99% confidence interval for the population mean u Table II Normal Curve Areas .03 .02 .04 .06 .01 .05 .00 .07 .08 .09 .0239 .0636 .1026 .1406 .1772 .2123 .0120 .0160 .0557 .0948 .0080 0199 .0596 .0987 .0000 .0398 .0793 .1179 .0040 .0438 .0832 .1217 .1591 .1950 .0279 67వ .1064 .0359 .0753 .1141 .1517 .1879 2224 .0319 .0714 .1103 0517 .0478 .0871 .0910 .1331 .1700 2054 .1480 .1844 2190 .1255 .1628 .1985 .1293 .1664 2019 .1443 .1808 2157 .1368 .1736 2088 .1554 .1915 2549 2852 3133 3389 3621 2486 2517 2823 3106 3365 3599 2324 2257 2291 2389 2422 .2734 3023 3289 3531 .2454 2357 2794 3078 3340 3577 .2580 2881 3159 3413 2764 3051 3315 3554 2611 2910 3186 3438 .2704 2995 3264 3508 2642 2939 3212 2673 2967 3238 3485 3461 1.0 3830 4015 3790 3810 3708 3907 4082 4236 4370 .3729 .3925 3686 3749 .3770 3665 3643 1.1 3997 4162 4306 .4429 3980 3962 4131 4279 4406 3849 4032 3888 4066 4222 4357 3944 3869 4049 4207 4345 1.2 1.3 4177 .4319 4441 4147 4292 4418 4099 4251 4382 4115 4265 4394 A192 4332 1.4 1.5 4545 4633 4706 .4767 4817 4525 .4616 4693 .4535 4625 4699 4761 4812 4495 4591 4671 4515 4505 4474 4573 4656 A726 4783 4484 4463 4452 1.6 4608 A686 4599 4678 4744 4798 A582 A664 4732 4788 4554 4641 4713 4772 4564 4649 4719 4778 1.7 1.8 1.9 2.0 .4756 4808 4750 4738 4803 4793 4857 4890 4916 4936 4952 4846 4881 4850 4884 4854 4842 4878 4906 4929 4946 4834 4871 4901 4925 4943 4838 4826 4864 4896 4920 4940 4830 4821 2.1 4887 4913 4934 4951 4875 4904 4927 4945 4868 4898 4922 4941 4861 4893 4918 4938 2.2 2.3 2.4 2.5 4909 4931 4948 .4911 .4932 4949 4964 4963 4973 4980 4986 4990 4960 4961 4971 4979 4985 4959 .4962 4957 4956 4967 4976 4982 4987 4955 4966 4975 4982 4987 4953 A965 4974 4981 4987 2.6 2.7 2.8 2.9 3.0 4974 4981 4986 4969 4977 .4984 .4988 4972 4979 4985 4989 4970 4978 4984 4989 4968 4977 4983 4988 శ990 .4989 Source: Abridged from Table 1 of A.Hald, Stutistical Tables and Formulas (New York: Wiley). 1952.

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

1. For a random sample of size n = 100 from a normally distributed population has a sample mean of x ̅ = 20.85 and a sample standard deviation of s = 13.41.

Find:

b. 99% confidence interval for the population mean μ

Table II
Normal Curve Areas
.03
.02
.04
.06
.01
.05
.00
.07
.08
.09
.0239
.0636
.1026
.1406
.1772
.2123
.0120
.0160
.0557
.0948
.0080
0199
.0596
.0987
.0000
.0398
.0793
.1179
.0040
.0438
.0832
.1217
.1591
.1950
.0279
67వ
.1064
.0359
.0753
.1141
.1517
.1879
2224
.0319
.0714
.1103
0517
.0478
.0871
.0910
.1331
.1700
2054
.1480
.1844
2190
.1255
.1628
.1985
.1293
.1664
2019
.1443
.1808
2157
.1368
.1736
2088
.1554
.1915
2549
2852
3133
3389
3621
2486
2517
2823
3106
3365
3599
2324
2257
2291
2389
2422
.2734
3023
3289
3531
.2454
2357
2794
3078
3340
3577
.2580
2881
3159
3413
2764
3051
3315
3554
2611
2910
3186
3438
.2704
2995
3264
3508
2642
2939
3212
2673
2967
3238
3485
3461
1.0
3830
4015
3790
3810
3708
3907
4082
4236
4370
.3729
.3925
3686
3749
.3770
3665
3643
1.1
3997
4162
4306
.4429
3980
3962
4131
4279
4406
3849
4032
3888
4066
4222
4357
3944
3869
4049
4207
4345
1.2
1.3
4177
.4319
4441
4147
4292
4418
4099
4251
4382
4115
4265
4394
A192
4332
1.4
1.5
4545
4633
4706
.4767
4817
4525
.4616
4693
.4535
4625
4699
4761
4812
4495
4591
4671
4515
4505
4474
4573
4656
A726
4783
4484
4463
4452
1.6
4608
A686
4599
4678
4744
4798
A582
A664
4732
4788
4554
4641
4713
4772
4564
4649
4719
4778
1.7
1.8
1.9
2.0
.4756
4808
4750
4738
4803
4793
4857
4890
4916
4936
4952
4846
4881
4850
4884
4854
4842
4878
4906
4929
4946
4834
4871
4901
4925
4943
4838
4826
4864
4896
4920
4940
4830
4821
2.1
4887
4913
4934
4951
4875
4904
4927
4945
4868
4898
4922
4941
4861
4893
4918
4938
2.2
2.3
2.4
2.5
4909
4931
4948
.4911
.4932
4949
4964
4963
4973
4980
4986
4990
4960
4961
4971
4979
4985
4959
.4962
4957
4956
4967
4976
4982
4987
4955
4966
4975
4982
4987
4953
A965
4974
4981
4987
2.6
2.7
2.8
2.9
3.0
4974
4981
4986
4969
4977
.4984
.4988
4972
4979
4985
4989
4970
4978
4984
4989
4968
4977
4983
4988
శ990
.4989
Source: Abridged from Table 1 of A.Hald, Stutistical Tables and Formulas (New York: Wiley). 1952.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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