Q1. interest y Consider the following bivariate data of an independent variable x and dependent variable of 4 6 (a) Calculate the mean, sample variance and sample standard deviations for x and y. Hint: Recall the formula for sample variance of x (¹)-(² n-1 n-1 (b) State the Chebyshev's and empirical rule for the proportion of samples that approximately lie within two standard deviations of the mean for the variable y. Clearly state the intervals and any assumptions. (e) The sample correlation coefficient is given by Σ(-2)(-9) VΣ(-2)(- 9)²" Calculater and comment on the relationship between x and y
Q1. interest y Consider the following bivariate data of an independent variable x and dependent variable of 4 6 (a) Calculate the mean, sample variance and sample standard deviations for x and y. Hint: Recall the formula for sample variance of x (¹)-(² n-1 n-1 (b) State the Chebyshev's and empirical rule for the proportion of samples that approximately lie within two standard deviations of the mean for the variable y. Clearly state the intervals and any assumptions. (e) The sample correlation coefficient is given by Σ(-2)(-9) VΣ(-2)(- 9)²" Calculater and comment on the relationship between x and y
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:STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z. score.
Z
.00
.01
0.0
0.1
0.2
50000
53983
57926
0.3 .61791
57535
.61409
.65173
.68793
.72240
.75490
.78524
93189
94408
95449
96327
.02
.03
.04
.05 .06
.07
.08
50399 50798 51197 51595 51994 52392 52790 53188
54380 54776 .55172 55567 .$5962 56356 56749 57142
58317 58706 .59095 59483 59871 60257 .60642 .61026
.62172 62552 .62930 .63307 .63683 64058 .64431 64803
0.4 .65542 .65910 .66276 .66640 .67003 .67364 67724 .68082 .68439
0.5 .69146 .69497 69847 .70194 .70540 .70884 .71226 .71566 .71904
0.6 .72575 72907 .73237 73565 .73891 .74215 74537 .74857 .75175
0.7 .75804 .76115 76424 .76730 .77035 .77337 77637 .77935 .78230
0.8 .78814 .79103 .79389 .79673 .79955 80234 80511 .80785 81057 81327
0.9 81594 .81859 82121 .82381 .82639 .82894 83147 .83398 83646 83891
1.0 .84134 .84375 .84614 .84849 .85083 .85314 85543 .85769 .85993 .86214
1.1 .86433 .86650 86864 .87076 .87286 .87493 87698 .87900 88100 .88298
1.2 .88493 88686
88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147
1.3 90320 90490 90658 90824 90988 .91149 91309 .91466 91621 91774
1.4 91924 92073 92220 92364 92507 92647 92785 92922 93056
1.5 93319 93448 93574
93699 .93822 .93943 94062
.94179 94295
1.6 94520 94630 94738 94845 94950 .95053 95154 .95254 95352
1.7 95543 95637 95728 .95818 .95907 .95994 96080
.96164 96246
1.8 96407 96485 96562 96638 96712
.96784 96856 .96926 96995 97062
1.9 97128 97193 97257 97320 97381 97441 97500 97558 97615 97670
2.0 .97725 97778 97831 97882 97932 .97982 98030 98077 98124 98169
2.1 98214 98257 98300 .98341 98382 .98422 98461 98500 98537 98574
2.2 .98610 98645 98679 98713 98745 .98778 98809 .98840 98870 98899
2.3 .98928 98956
.99010 .99036 .99061 99086 99111 .99134 .99158
2.4 .99180
99245 99266 99286 99305 99324 99343 99361
2.5 .99379
99430 99446 .99461 99477 99492 99506 99520
2.6 .99534 99547 99560 99573 .99585 .99598 99609 .99621 99632 99643
.99653
99664
99674 .99683 99693 .99702 99711 .99720 99728 99736
2.8 .99744 99752 99760 99767 99774 99781 99788 99795 99801 99807
2.9
99813 99819 99825 99831 99836 99841
99846 99851 99856 .99861
3.0 99865 99869 99874 99878 99882 99886 99889 99893 99896 99900
3.1 99903 99906 99910 .99913 .99916 .99918 99921 99924 99926 .99929
3.2 .99931 99934 99936 99938 99940
99942 99944 99946 99948 99950
.99936 .99938 99940 .99942 .99944 .99946
.99955 .99957 99958 99960
99971 .99972
98983
99224
99202
99396 99413
2.7
.99970
.99979
99980
.99986
.99986
.99990
99993 .99994
99996
3.2
3.3
3.4
3.5
3.6
353
.99931
.99934
.99952
99953
.99966
99968
.99969
.99977
99978 .99978
.99984
99985 99985
3.7
.99989
99990 .99990
3.8 99993
99993
3.9 99995 99995 99996
.99948
.99950
99961 99962 .99964 .99965
99973 .99974 99975 99976
99983
99989
99981 .99982 99983
99988 99988
99992 99992 .99992
.99981
99987 99987
99991
.99991 99992
99994 99994
99996 99996
.09
53586
99994 99995
.99996
99996
.99995 99995
99997 99997
Transcribed Image Text:Q 1.
interest y
Consider the following bivariate data of an independent variable x and dependent variable of
x 00112 3 4 6
y 32100-1 -2 -15
(a) Calculate the mean, sample variance and sample standard deviations for x and y.
Hint: Recall the formula for sample variance of x
Σ. (2-2) (Σ., 3) - (Σ., «
n-1
n-1
(b) State the Chebyshev's and empirical rule for the proportion of samples that approximately lie within
two standard deviations of the mean for the variable y. Clearly state the intervals and any assumptions.
(c) The sample correlation coefficient is given by
Σ(-2)(-9)
νΣ. (π. – 2) Σ (m - 57)2
Calculater and comment on the relationship between x and y.
-2.2
r=
Appendix
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z. score.
Z
.00
.01
J02
.04
48
.05 .06
00004 00004 00004
00006 00006
00009 00008
07
00004 00003
.00005 00005
00008 00008
00013 00013 00012 00012
00019
00018 00017
00027 00026 00025
00039 .00038 00036
00058
00056
00054
00052
00082
00079 00076 00074
00071
00118
00114
00111 00107 00104
00100
00164
00159
00154 .00149 00144 .00139
-3.9 00005 00005 00004 00004
-3.8 00007 00007
00007 00006 00006
-3.7 00011 00010 00010 00010 00009
-3.6 00016 00015 00015 00014 00014
-3.5 00023 00022 00022 00021 00020 00019
-3.4 00034 00032 ,00031 00030 00029 00028
00048 00047 00045 00043 00042 00040
-3.2 00069 00066 00064 00062 00060
-3.1 00097 00094 00090 .00087 00084
00135 00131 00126 00122
-2.9 00187 00181 00175 .00169
-2.8 00256 00248
00240 00233 00226 00219 00212 00205 .00199 .00193
-2.7 00347 00336 00326 00317 00307 00298 00289 00280 00272 00264
-2.6 00466 00453 00440 00427 00415 00402 00391 00379 00368 00357
-2.5 00621 00604 00587 00570 00554 00539 00:23 00508 00494 .00480
00820 00798
00776 00755 00734 00714 00695 00676 00657 00639
01072 01044
01017 .00990 00964 00939 00914 00889
00866 00842
01390 01355 01321 01287 01255 01222 01191 01160
01786 01743
01700 01659 01618 01578 01539 01500
-2.0 02275 02222 02169 02118 02068 02018 01970 01923
-1.9 02872 02807 02743 02680 02619 02559 02500
03593 03515 03438
03362 03288 03216 03144
-1.7 04457 04363 04272 04182 04093
04006 03920
-1.6 05480 05370 05262 05155 05050 04947
-1.5 06681 06552 06426 06301 06178
06057
05821 05705 05592
07636
07493
07353 07215 07078 06944 .06811
09680 09510 09342 09176
09012 08851 08691 08534 08379
08226
-1.2 11507 11314 11123 10935 10749 -10565 .10383 .10204 10027 09853
12714
-14917 14686 14457
03673
04551
04846
05938
-1.4 08076 07927 07780
-1.1 13567 13350 13136 12924
-1.0 15866 .15625 .15386 15151
12507 12302 12100 11900 11702
14231
14007
13786
45224 44828
01130
01463
01876
02442
02385
03074 03005
01836
04746 04648
03754
.09
.00003
.00005
.00008
00011
00017
.00024
.00035
00050
01101
01426
01831
02330
02938
.16109
.18673
21476
-0.9
.18406 18141 .17879 17619 .17361 .17106 16853 .16602 .16354
-0.8 21186 20897 20611 20327 20045 .19766 19489 .19215 .18943
-0.7 24196 23885 23576 23270 22965 .22663 22363 .22065 21770
-0.6 27425 27093 26763 26435 26109
25785
25463 25143 24825 24510
-0.5 30854 30503 30153 29806 29460 29116 28774 28434 28096 27760
-0.4 34458 34090 33724 33360 32997 .32636 32276 31918 31561 31207
37448
.36317
35197
37070
36693
35942 .35569
34827
38209 37828
42074 41683 41294
40905
40517
40129
39743 39358 38974
38591
-0.3
-0.2
-0.1 46017 45620
-0.0 50000 49601
44433
44038 43644
43251 42858
42465
49202 48803 48405 48006 47608
47210
46812
46414
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps
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