Figure 6.4b (p. 172) plotted the sampling distribution of the mean from 200 samples of size 5 from the population of 1000 birthweights given in Table 6.2. The mean of the 1000 birthweights in Table 6.2 is 112.0 oz with standarddeviation 20.6 oz.A) If the central-limit theorem holds, what proportion of the sample means should fall within 0.5 lb of the population mean (112.0 oz)?B) Answer Problem 6.52 for 1 lb rather than 0.5 lb.C) Compare your results in Problems 6.52 and 6.53 with the actual proportion of sample means that fall in these ranges.D) Do you feel the central-limit theorem is applicable for samples of size 5 from this population? Explain. TABLE 6.2Sample of birthweights (oz) obtained from 1000 consecutivedeliveries at Boston City HospitalID0 1 2 3 4 5 6 7 8 9 10 11 12Numbers13 14 15 16 17 18 19000-019116 124 119 100 127 103 14082 107 132 1009276 129 138 128 115 133 70 121020-039114 114 121 107 120 1238396 116 1107186 136 118 120 110 107 1578971040-05998 105 10652 123 101 111 130 12994 124 127 128 1128395 118 11586 120060-079106 115 100 107 131 114 121 110 11593 11676 138 126 14393 121 13581 135080-099108 152 127 118 110 115 109 133 116 129 118 126 137 11032 139 132 110 140 119100-119109 108 1038887 144 105 138 115 104 129 10892 100 14593 11585 124 123120-13914196 146 115 124 11398 110 153 165 140 13279 101 127 137 129 144 126 155140-159120 128 119 108 11393 144 12489 12687 1209960 11586 14397 106 148160-179113 135 117 129 120 11792 11880 132 121 11957 126 12677 135 130 102 107180-199115 135 112 12189 135 127 115 1336491 1267885 10694 122 111 10989200-21999 118 104 10294 113 124 118 104 124 13380 117 112 112 112 102 118 107 104220-23990 113 132 12289 111 118 108 148 103 112 12886 111 140 126 143 120 124 110240-25914292 132 12897 13299 131 120 106 115 101 130 120 13089 107 15290 116260-279106 111 120 198 123 152 13583 10755 131 108 100 104 112 121 102 114 102 101280-299118 114 112 133 139 11377 109 142 144 114 117979693 120 149 107 107 117300-31993 103 121 118 11089 127 100 156 106 122 10592 128 124 125 118 113 110 149320-3399898 141 13192 141 110 1349088 111 1376795 10275 108 11899 79340-359110 124 122 104 13398 108 125 106 128 13295 11467 134 136 138 122 103 113360-379142 121 125 11197 127 117 122 12080 114 126 10398 108 100 10698 116 109380-3999897 129 114 102 128 107 11984 117 119 128 121 113 128 111 112 120 1229190400-419117 100 108 101 144 104 110 146 117 107 126 120 104 129 147 111 106 13897420-439120 11794 116 119 108 109 106 134 121 125 105 177 109 109 10979 11892 103440-45911095 111 144 130839381 116 115 131 135 11697 108 103 134 14072 112460-479101 111 129 128 10890 11399 10341 129 104 144 12470 106 118998593480-499100 105 104 113 10688 102 125 132 123 160 100 128 13149 102 110 10696 116500-519128 102 124 110 129 102 101 119 101 119 141 112 100 105 155 1246794 134 123520-539925617 135 141 105 133 118 117 1128792 104 104 132 121 118 126 11490540-55910978 117 165 127 122 108 109 11998 120 1019676 14383 100 128 124 137560-57990 12989 125 131 11872 12191 11391 137 110 137 111 135 10588 112 104580-599102 122 144 114 120 136 14498 108 130 11997 142 115 129 125 109 103 114 106600-619109 1198998 104 11599 138 12291 16196 138 14032 132 10892 11858620-639158 127 12175 112 121 14080 12573 115 12085 10495 106 1008799 113640-65995 146 12658 64 1376990 104 124 120628396 126 155 133 115 97 105660-67911778 10599 12386 126 121 10997 131 133 121 125 12097 10192 111 119680-69911780 145 128 14097 126 109 113 125 15797 119 103 102 128 11696 109 112700-71967 121 116 126 106 11677 119 119 122 109 117 127 114 1027588 11799 136720-739127 136 10397 130 129 128 11922 109 145 12996 128 122 115 102 127 109 120740-759111 114 115 112 146 100 106 137 48 110 97 103 104 107 12387 14089 112 123760-779130 123 125 124 135 11978 125 103556983 106 130988192 110 112 104780-799118 107 117 123 138 130 10078 146 137 11461 132 109 133 132 120 116 133 133800-81986 116 101 124 1269493 132 126 10798 102 13559 137 120 119 106 125 122820-839101 1199786 105 14089 13974 131 1189198 121 102 115 115 135 10090840-859110 113 136 140 129 117 117 129 14388 105 110 123879799 128 128 110 132860-87978 128 12693 148 12195 121 12780 109 105 136 141 10395 140 115 118 117880-899114 109 144 119 127 116 103 144 117 13174 109 117 100 103 12393 107 113 144900-91999 17097 135 11589 120 106 141 137 107 132 13258 113 102 12098 104 108920-93985 115 1088988 126 122 10768 121 113 116948593 132 14698 132 104940-959960-979102 116 108 107 121 132 105 114 107 121 101 110 137 122 102 125 104 124 121 11110193938872 142 118 157 1215892 114 104 1199152 110 116 100 147980-99911499 123977981 14692 126 12272 1539789 100 104 1248381 129 138 8 8 8 8 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 2 4 6 8 0 2 4 6 8 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 40 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0(b) n = 5Birthweight (b) in oz% of samples with birthweight = b으2109876543210

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Description: Figure 6.4b (p. 172) plotted the sampling distribution of the mean from 200 samples of size 5 from the population of 1000 birthweights given in Table 6.2. The mean of the 1000 birthweights in Table 6.2 is 112.0 oz with standarddeviation 20.6 oz.A) If

The central limit theorem can be stated as follows; "Suppose we draw a random sample of…

Answered: Figure 6.4b (p. 172) plotted the…

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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Figure 6.4b (p. 172) plotted the sampling distribution of the mean from 200 samples of size 5 from the population of 1000 birthweights given in Table 6.2. The mean of the 1000 birthweights in Table 6.2 is 112.0 oz with standard
deviation 20.6 oz.

A) If the central-limit theorem holds, what proportion of the sample means should fall within 0.5 lb of the population mean (112.0 oz)?

B) Answer Problem 6.52 for 1 lb rather than 0.5 lb.

C) Compare your results in Problems 6.52 and 6.53 with the actual proportion of sample means that fall in these ranges.

D) Do you feel the central-limit theorem is applicable for samples of size 5 from this population? Explain.

TABLE 6.2
Sample of birthweights (oz) obtained from 1000 consecutive
deliveries at Boston City Hospital
ID
0 1 2 3 4 5 6 7 8 9 10 11 12
Numbers
13 14 15 16 17 18 19
000-019
116 124 119 100 127 103 140
82 107 132 100
92
76 129 138 128 115 133 70 121
020-039
114 114 121 107 120 123
83
96 116 110
71
86 136 118 120 110 107 157
89
71
040-059
98 105 106
52 123 101 111 130 129
94 124 127 128 112
83
95 118 115
86 120
060-079
106 115 100 107 131 114 121 110 115
93 116
76 138 126 143
93 121 135
81 135
080-099
108 152 127 118 110 115 109 133 116 129 118 126 137 110
32 139 132 110 140 119
100-119
109 108 103
88
87 144 105 138 115 104 129 108
92 100 145
93 115
85 124 123
120-139
141
96 146 115 124 113
98 110 153 165 140 132
79 101 127 137 129 144 126 155
140-159
120 128 119 108 113
93 144 124
89 126
87 120
99
60 115
86 143
97 106 148
160-179
113 135 117 129 120 117
92 118
80 132 121 119
57 126 126
77 135 130 102 107
180-199
115 135 112 121
89 135 127 115 133
64
91 126
78
85 106
94 122 111 109
89
200-219
99 118 104 102
94 113 124 118 104 124 133
80 117 112 112 112 102 118 107 104
220-239
90 113 132 122
89 111 118 108 148 103 112 128
86 111 140 126 143 120 124 110
240-259
142
92 132 128
97 132
99 131 120 106 115 101 130 120 130
89 107 152
90 116
260-279
106 111 120 198 123 152 135
83 107
55 131 108 100 104 112 121 102 114 102 101
280-299
118 114 112 133 139 113
77 109 142 144 114 117
97
96
93 120 149 107 107 117
300-319
93 103 121 118 110
89 127 100 156 106 122 105
92 128 124 125 118 113 110 149
320-339
98
98 141 131
92 141 110 134
90
88 111 137
67
95 102
75 108 118
99 79
340-359
110 124 122 104 133
98 108 125 106 128 132
95 114
67 134 136 138 122 103 113
360-379
142 121 125 111
97 127 117 122 120
80 114 126 103
98 108 100 106
98 116 109
380-399
98
97 129 114 102 128 107 119
84 117 119 128 121 113 128 111 112 120 122
91
90
400-419
117 100 108 101 144 104 110 146 117 107 126 120 104 129 147 111 106 138
97
420-439
120 117
94 116 119 108 109 106 134 121 125 105 177 109 109 109
79 118
92 103
440-459
110
95 111 144 130
83
93
81 116 115 131 135 116
97 108 103 134 140
72 112
460-479
101 111 129 128 108
90 113
99 103
41 129 104 144 124
70 106 118
99
85
93
480-499
100 105 104 113 106
88 102 125 132 123 160 100 128 131
49 102 110 106
96 116
500-519
128 102 124 110 129 102 101 119 101 119 141 112 100 105 155 124
67
94 134 123
520-539
92
56
17 135 141 105 133 118 117 112
87
92 104 104 132 121 118 126 114
90
540-559
109
78 117 165 127 122 108 109 119
98 120 101
96
76 143
83 100 128 124 137
560-579
90 129
89 125 131 118
72 121
91 113
91 137 110 137 111 135 105
88 112 104
580-599
102 122 144 114 120 136 144
98 108 130 119
97 142 115 129 125 109 103 114 106
600-619
109 119
89
98 104 115
99 138 122
91 161
96 138 140
32 132 108
92 118
58
620-639
158 127 121
75 112 121 140
80 125
73 115 120
85 104
95 106 100
87
99 113
640-659
95 146 126
58 64 137
69
90 104 124 120
62
83
96 126 155 133 115 97 105
660-679
117
78 105
99 123
86 126 121 109
97 131 133 121 125 120
97 101
92 111 119
680-699
117
80 145 128 140
97 126 109 113 125 157
97 119 103 102 128 116
96 109 112
700-719
67 121 116 126 106 116
77 119 119 122 109 117 127 114 102
75
88 117
99 136
720-739
127 136 103
97 130 129 128 119
22 109 145 129
96 128 122 115 102 127 109 120
740-759
111 114 115 112 146 100 106 137 48 110 97 103 104 107 123
87 140
89 112 123
760-779
130 123 125 124 135 119
78 125 103
55
69
83 106 130
98
81
92 110 112 104
780-799
118 107 117 123 138 130 100
78 146 137 114
61 132 109 133 132 120 116 133 133
800-819
86 116 101 124 126
94
93 132 126 107
98 102 135
59 137 120 119 106 125 122
820-839
101 119
97
86 105 140
89 139
74 131 118
91
98 121 102 115 115 135 100
90
840-859
110 113 136 140 129 117 117 129 143
88 105 110 123
87
97
99 128 128 110 132
860-879
78 128 126
93 148 121
95 121 127
80 109 105 136 141 103
95 140 115 118 117
880-899
114 109 144 119 127 116 103 144 117 131
74 109 117 100 103 123
93 107 113 144
900-919
99 170
97 135 115
89 120 106 141 137 107 132 132
58 113 102 120
98 104 108
920-939
85 115 108
89
88 126 122 107
68 121 113 116
94
85
93 132 146
98 132 104
940-959
960-979
102 116 108 107 121 132 105 114 107 121 101 110 137 122 102 125 104 124 121 111
101
93
93
88
72 142 118 157 121
58
92 114 104 119
91
52 110 116 100 147
980-999
114
99 123
97
79
81 146
92 126 122
72 153
97
89 100 104 124
83
81 129

13
8 8 8 8 8 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 2 4 6 8 0 2 4 6 8 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4
0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0
(b) n = 5
Birthweight (b) in oz
% of samples with birthweight = b
으2109876543210

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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