Question 2: Answer the following questions referring to the MINITAB simulation of confidence intervals given in the photo below"In theory, how many of the intervals would you expect to contain the true population mean U ( = 10)?How many of the intervals actually contain the mean of the population?If this simulation were repeated would you always find that the same number of intervals contain U? MTBrandom 25 c1-c40;The first two commands on the left select 40 random sampleseach of size n = 25, from a Normal distribution with u = 10,SUBC> norm 10 1.5.and o= 1.5.МТВzint 95 1.5 c1-c40The third command forms the 95% Z-interval for each sampleConfidence IntervalsThe assumed sigma1.50VariablenMeanSt DevSE Mean95.0 % C.I.10.698)10.980)9.522,9.804,9.502,9.046,8.830,C110.1101.0910.300C22510.3921.6580.30010.679)10.222)10.007)2510.0911.3230.300259.6341.3730.300259.4181.7000.3002510.9361.5620.30010.348,11.524) x10.4290.30011.017)10.377)10.356)251.2009.841,9.200,9.180,9.897,9.616,259.7881.6480.300259.7681.7440.300C102510.4851.5970.30011.074)C112510.2040.9640.30010.792)10.284,9.408,9.616,9.337,9.162,9.748,8.942,0.30011.460) x10.584)10.793)C122510.8721.338C13259.9961.4510.300C142510.2041.6480.300C15259.9251.6770.30010.513)C16259.7501.6330.30010.339)C172510.3371.4180.30010.925)C18259.5301.3360.30010.118)C19259.3311.3040.3008.743,9.565,9.202,9.403,9.325,8.831,9.443,9.450,9.592,9.708,9.259,9.593,9.320,9.624,9.492,9.472,9.428,9.949,9.491,9.919) x10.741)10.378)C202510.1531.7330.300C21259.7901.5820.300C22259.9911.3000.30010.579)C23259.9131.2210.30010.501)10.007)C24259.4191.3890.300C252510.0311.4980.30010.619)10.627)10.769)10.884)C262510.0391.5310.300C272510.1801.7110.300C282510.2961.3140.300C29259.8471.4630.30010.435)10.1820.30010.770)10.497)C30251.371C319.9081.5260.300C322510.2121.6940.30010.800)10.669)10.648)10.604)11.125)C332510.0801.2910.300C342510.0601.5340.300C352510.0161.6440.300C362510.5371.4010.300C372510.0791.6410.30010.667)10.2581.7030.30010.846)9.670,9.254,9.820,C3810.430)10.996)C39259.8422.2500.300C402510.4081.2840.300E LO LO LOLO LO LO LON N N N N N N N N N N

Introduction: The true population mean is given as, μ = 10. The simulated 95% confidence intervals…

Answered: Answer the following questions…

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 2: Answer the following questions referring to the MINITAB simulation of confidence intervals given in the photo below"

In theory, how many of the intervals would you expect to contain the true population mean U ( = 10)?
How many of the intervals actually contain the mean of the population?
If this simulation were repeated would you always find that the same number of intervals contain U?

MTB
random 25 c1-c40;
The first two commands on the left select 40 random samples
each of size n = 25, from a Normal distribution with u = 10,
SUBC> norm 10 1.5.
and o= 1.5.
МТВ
zint 95 1.5 c1-c40
The third command forms the 95% Z-interval for each sample
Confidence Intervals
The assumed sigma
1.50
Variable
n
Mean
St Dev
SE Mean
95.0 % C.I.
10.698)
10.980)
9.522,
9.804,
9.502,
9.046,
8.830,
C1
10.110
1.091
0.300
C2
25
10.392
1.658
0.300
10.679)
10.222)
10.007)
25
10.091
1.323
0.300
25
9.634
1.373
0.300
25
9.418
1.700
0.300
25
10.936
1.562
0.300
10.348,
11.524) x
10.429
0.300
11.017)
10.377)
10.356)
25
1.200
9.841,
9.200,
9.180,
9.897,
9.616,
25
9.788
1.648
0.300
25
9.768
1.744
0.300
C10
25
10.485
1.597
0.300
11.074)
C11
25
10.204
0.964
0.300
10.792)
10.284,
9.408,
9.616,
9.337,
9.162,
9.748,
8.942,
0.300
11.460) x
10.584)
10.793)
C12
25
10.872
1.338
C13
25
9.996
1.451
0.300
C14
25
10.204
1.648
0.300
C15
25
9.925
1.677
0.300
10.513)
C16
25
9.750
1.633
0.300
10.339)
C17
25
10.337
1.418
0.300
10.925)
C18
25
9.530
1.336
0.300
10.118)
C19
25
9.331
1.304
0.300
8.743,
9.565,
9.202,
9.403,
9.325,
8.831,
9.443,
9.450,
9.592,
9.708,
9.259,
9.593,
9.320,
9.624,
9.492,
9.472,
9.428,
9.949,
9.491,
9.919) x
10.741)
10.378)
C20
25
10.153
1.733
0.300
C21
25
9.790
1.582
0.300
C22
25
9.991
1.300
0.300
10.579)
C23
25
9.913
1.221
0.300
10.501)
10.007)
C24
25
9.419
1.389
0.300
C25
25
10.031
1.498
0.300
10.619)
10.627)
10.769)
10.884)
C26
25
10.039
1.531
0.300
C27
25
10.180
1.711
0.300
C28
25
10.296
1.314
0.300
C29
25
9.847
1.463
0.300
10.435)
10.182
0.300
10.770)
10.497)
C30
25
1.371
C31
9.908
1.526
0.300
C32
25
10.212
1.694
0.300
10.800)
10.669)
10.648)
10.604)
11.125)
C33
25
10.080
1.291
0.300
C34
25
10.060
1.534
0.300
C35
25
10.016
1.644
0.300
C36
25
10.537
1.401
0.300
C37
25
10.079
1.641
0.300
10.667)
10.258
1.703
0.300
10.846)
9.670,
9.254,
9.820,
C38
10.430)
10.996)
C39
25
9.842
2.250
0.300
C40
25
10.408
1.284
0.300
E LO LO LO
LO LO LO LO
N N N N N N N N N N 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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