3. Carry out a sampling of the jurisdictions by using a random number generator

Question

3. Carry out a sampling of the jurisdictions by using a random number generator as shown in class to select a simple random sample of size n=20 from the full list of the jurisdictions. Provide the selected sample of 20 in the table included below, making sure to include the corresponding percent of low-income working families (%LIWF) information for each jurisdiction selected.

2011 Data Percent of low income working families (<200% poverty level) Percent of 18-64 yr olds with no HS diploma Alabama 37.3 15.3 Alaska 25.9 8.6 Arizona 38.9 14.8 Arkansas 41.8 14.0 California 34.3 17.6 Colorado 27.6 10.1 Connecticut 21.1 9.5 Delaware 27.8 11.9 District of Columbia 23.2 10.8 Florida 37.3 13.1 Georgia 36.6 14.9 Hawaii 25.8 7.2 Idaho 38.6 10.7 Illinois 30.4 11.5 Indiana 31.9 12.2 Iowa 28.8 8.1 Kansas 32.0 9.7 Kentucky 34.1 13.6 Louisana 36.3 16.1 Maine 30.4 7.1 Maryland 19.5 9.7 Massachusetts 20.1 9.1 Michigan 31.6 10.0 Minnesota 24.2 7.3 Mississippi 43.6 17.0 Missouri 32.7 11.1 Montana 36.0 7.0 Nebraska 31.1 8.7 Nevada 37.4 16.6 New Hampshire 19.7 7.3 New Jersey 21.2 10.1 New Mexico 43.0 16.2 New York 30.2 13.0 North Carolina 36.2 13.6 North Dakota 27.2 5.9 Ohio 31.8 10.3 Oklahoma 37.4 13.2 Oregon 33.9 10.8 Pennsylvania 26.0 9.4 Rhode Island 26.9 12.0 South Carolina 38.3 14.2 South Dakota 31.0 8.7 Tennessee 36.6 12.7 Texas 38.3 17.8 Utah 32.3 9.9 Vermont 26.2 6.6 Virginia 23.3 10.2 Washington 26.4 10.2 West Virginia 36.1 12.9 Wisconsin 28.7 8.5 Wyoming 28.1 8.0

Explanation / Answer

We have 51 entries (or rows) from which we have to sample 20 numbers.

We randomly generate 20 numbers without replacement from 51 numbers.

And then the entries corresponding to those 20 numbers is our sample.

We use R to generate 20 random numbers from 51.

As follows-

sample(51, 20)

The randomly generated 20 numbers are:

31 37 46 10 32 28 2 23 13 4 26 48 47 35 33 42 3 16 24 9

And thus, the sample is:

X Percent.of.low.income.working.families...200..poverty.level. Percent.of.18.64.yr.olds.with.no.HS.diploma
31 New Jersey 21.2 10.1
37 Oklahoma 37.4 13.2
46 Vermont 26.2 6.6
10 Florida 37.3 13.1
32 New Mexico 43.0 16.2
28 Nebraska 31.1 8.7
2 Alaska 25.9 8.6
23 Michigan 31.6 10.0
13 Idaho 38.6 10.7
4 Arkansas 41.8 14.0
26 Missouri 32.7 11.1
48 Washington 26.4 10.2
47 Virginia 23.3 10.2
35 North Dakota 27.2 5.9
33 New York 30.2 13.0
42 South Dakota 31.0 8.7
3 Arizona 38.9 14.8
16 Iowa 28.8 8.1
24 Minnesota 24.2 7.3
9 District of Columbia 23.2 10.8

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