Question

In: Math

1. Draw two histograms to represent two populations with a common mean, but with a standard...

1. Draw two histograms to represent two populations with a common mean, but with a standard deviation

of the second population larger than that of the first.

2. Draw two histograms to represent two populations with the mean of the first population larger than

that of the second, but with a common standard deviation.

3. If the standard deviation of a population is zero, what can you say about the observations of that

population?

( Please explain the solutions . i have a test this week and I’m confused )

Expert Solution

a.

Here we are taking samples of two normal distribution with the same mean and different standard deviation.

data1 ~ N(5,10) and data2 ~ N(5,20)

and the data is as follows

> data1 <- rnorm(20,5,10)
> data2 <- rnorm(20,5,20)
> hist(data1)
> hist(data2)
> data1
[1] -14.1594520 -2.8567743 4.0020726 5.0485712 -1.4288060 4.1153539 17.3823061
[8] 3.3351271 4.4581816 -10.7527625 -0.3584677 7.5337611 1.0341276 -7.6230778
[15] 8.4608876 -6.2248454 5.9739155 2.8561372 10.6726384 19.2082070
> data2
[1] -27.7207000 2.6669421 -12.1278855 -36.4089068 -3.2887953 -11.7676573 8.3062198
[8] 8.8320770 -1.1073838 8.3325758 -0.6989467 24.3139753 -14.8585661 0.3552415
[15] 5.2751997 -17.3715020 -9.2753353 30.0987542 -34.5395722 47.1727001

b.

Here we are taking samples of two normal distribution with the different mean and same standard deviation.

data1 ~ N(15,5) and data2 ~ N(10,5)

and the data is as follows

data1 <- rnorm(20,15,5)
> data2 <- rnorm(20,10,5)
> hist(data1)
> hist(data2)
> data1
[1] 8.839760 16.676272 19.904197 16.375453
[5] 19.135349 10.804172 8.823600 5.251564
[9] 15.876402 18.467850 11.928616 8.947840
[13] 17.646653 17.692819 1.367342 17.655593
[17] 16.720890 17.693406 21.057683 21.289203
> data2
[1] 11.5368136 9.6833670 5.9658488
[4] 8.4530015 10.5477951 18.9525564
[7] 15.9885261 15.1161655 15.4226111
[10] 9.7654731 3.0236538 16.4022282
[13] 11.1879639 -0.6999328 5.2688426
[16] 15.2005260 15.2470598 3.6663033
[19] 15.0583669 10.2965091

c.

If the standard deviation of a sample is zero, we can say that the observation of the sample are identical to each other

d <- rnorm(10,5,0)
> d
[1] 5 5 5 5 5 5 5 5 5 5

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