Suppose X,n} is a sequence of random variables draw from an underlying popu-lation space, then the sample mean of {Xn} defined as Xnin distribution to Normal Distribution N(u, a2), where u E[X3], o2:E1Xi, convergeVar[X Plot the histogram of 2000 sample mean X10 together with N(20, 2). Whatis your conclusion from the graph.

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Asked Nov 20, 2019
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Suppose X,n} is a sequence of random variables draw from an underlying popu-
lation space, then the sample mean of {Xn} defined as Xn
in distribution to Normal Distribution N(u, a2), where u E[X3], o2:
E1Xi, converge
Var[X
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Suppose X,n} is a sequence of random variables draw from an underlying popu- lation space, then the sample mean of {Xn} defined as Xn in distribution to Normal Distribution N(u, a2), where u E[X3], o2: E1Xi, converge Var[X

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Plot the histogram of 2000 sample mean X10 together with N(20, 2). What
is your conclusion from the graph.
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Plot the histogram of 2000 sample mean X10 together with N(20, 2). What is your conclusion from the graph.

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Expert Answer

Step 1

From the given information, the sample mean X10-bar follows normal distribution N(20, 25/10).

That is, µ=20 and

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25 10 25 V10 1.58

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Step 2

Generating 2000 sample means from the normal distribution with mean 20 and the standard deviation 1.58.

 

Excel Procedure:

 

  1. Go to Data
  2. Click on Data Analysis.
  3. Select ‘Random number generation’ and click on ‘OK’.
  4. Enter 1 for ‘Number of variables’.
  5. Enter 2000 for ‘Number of random numbers’.
  6. Select ‘Normal’ under ‘Distribution’.
  7. Enter 20 for mean.
  8. Enter 58 for standard deviation.
  9. Click on ‘OK’.

 

Excel Output:

 

Here, there are more number of samples. Therefore, entire samples cannot be displayed:

 

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A В C D E F G 1 19.97311 16.57696 20.36777 21.64006 19.86853 18.38684 19.87313 20.38219 21.46774 19.83076 20.07866 21.37234 18.47106 20.80701| 3 18.00937 22.375 25 18.18902 22.09314 20.93349 18.39293 17.43677 22.93423 21.0818 21.53378 18.28127 21.93929 18.99413 22.22762 18.67309 17.76551 20.18213 16.75574 23.12288 21.16379 21.49645 6 20.18347 20.1898 19.8678 21.89562 19.88501 18.17849 17.70958 7 19.28476 22.10864 19.34267 20.23492 20.72691 21.50252 19.6705 18.72752 20.84972 22.14635 21.54135 20.55762 20.85014 20.80384 19.4924 20.50315 21.57119 19.14818 20.22283 20.86681 21.2886 0 19.88126 20.43255 22.58741 24.18248 19.10467 20.03669 20.58692 1 21.29079 22.34428 22.34682 19.25814 19.97153 17.58819 19.36279 2 19.48922 18.2597 20.44222 20.29167 20.57864 21.66407 22.00406 13 19.34083 20.12553 20.14142 18.2126 20.00369 20.61864 20.15368 4 21.15225 18.79426 21.70807 17.238 20.51754 20.65838 19.77497 15 20.76624 19.10991| 18.1488 19.91444 21.12592 18.55095 20.10554 16 19.08215 21.65966 20.10808 19.70095 19.80826 18.72802 20.17179 17 17.1799 21.77918 20.28946 23.01306 20.81225 18.65269 18.7847 18 21.7207 18.64258 20.61786 18.45515 21.13763 25.41508 22.2709 9 19.84874 16.71487 18.84854 20.45619 19.69701 21.36407 19.37025 20 21.76873 21.81028 18.24544 18.06506 20.1904 21.01016 21.13419 21 18.89224 20.63997 20.82635 21.37905 19.11571 19.59449 18.32197 2 18.70329 21.20849 18.05711 19.90452 22.93492 15.91041 20.27337 3 23.06216 22.66787 19.28824 20.8514 16.70642 17.34413 20.7127 19.81605 19.85797 20.09306 19.0489 20.89817 23.47272 19.95304 4 5 21.76941 19.41191 19.29425 19.81702 18.76034 20.16778 19.4088 6 22.52826 19.20028 19.6429 21.2918 17.28891 20.17763 18.85735

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Step 3

The histogram is constructed below:

 

Steps to construct box plot:

 

  • Select the 2000 random numbers.
  • Go to Insert.
  • Select histogram under ...
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Histogram 300 250 200 150 100 50 0 15.56541297, (15.99541297. (16.42541297... (16.85541297.. (17.28541297.. (17.71541297,. (18.14541297,. (18.57541297 (19.00541297 (19.43541297,. (19.86541297 (20.29541297p. (20.72541297, (21.15541297, (21.58541297 (22.01541297, (22.44541297 (22.87541297 (23.30541297 (23.73541297,.. (24.16541297,. (24.59541297,. (25.02541297,..

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