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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

100 samples were obtained from a normal population with means = 50 and variance = 4. For each sample complete the data in the table, construct the respective interval of confidence and identify if the value of the population mean is contained in said interval. (image)

The table is much longer, but you don't have to do it all. With the procedure or code of some examples it is enough to guide me with the whole table. My biggest doubt is how to find the lower and upper intervals, because I have formulated the problem several times but they give me different results. Should a t-distribution or a normal distribution be used? What formula?

the entire table contains 100 samples

Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
X1
40
53
57
44
48
58
51
50
59
52
51
52
47
52
54
51
X2
55
55
48
50
59
41
46
47
54
44
45
48
50
54
44
43
X3
45
50
46
55
51
46
51
51
49
46
53
58
53
50
51
49
X4
53
53
50
47
49
56
40
52
49
57
54
57
58
49
43
51
X5
41
51
46
44
51
46
49
51
49
43
46
56
47
53
46
46
X6
50
43
48
44
47
55
47
51
41
46
48
44
44
43
52
49
X7
54
54
53
47
47
49
48
60
56
50
49
52
48
53
53
48
X8
60
53
51
59
45
50
60
53
46
50
46
50
47
59
58
46
X9
56
50
47
53
55
51
46
48
56
47
41
49
48
49
47
48
sample mean
lower limit Upper Limit
contains mu? y/n

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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