Frankfort-Nachmias & Anna Leon-Guerrero-Social Statistics for a Diverse Society ( 8th ED)

There is only one problem this week, but it may take some time. Show your work for full credit.

Do states with high crime rates have high Incarceration rates? I drew a systematic random sample of 17 states. (See pages 155-156 in the text.) The table below shows Crime Rate data, as reported by the FBI and Incarceration Rate data as reported by the Bureau of Justice Statistics for the most recent years for which data were available. for those states. I have arranged the data performed the calculations shown in Table 12.2 on page 331.

Total crime Incarceration Rate
Rate (X) per 100,000 Adults (Y) X- Mean X (X-Mean X)2 (Y-Mean Y) (Y-MeanY)2 X-Mean X) * (Y-Mean Y)
2016 2015
State
Alabama 4157.2 790 4157.20 ########## 790.00 624100.00 3284188
Arkansas 3819.5 774 3819.50 ########## 774.00 599076.00 2956293
Connecticut 2035.1 396 2035.10 4141632.01 396.00 156816.00 805899.6
Florida 3117.1 621 3117.10 9716312.41 621.00 385641.00 1935719.1
Idaho 1974.5 590 1974.50 3898650.25 590.00 348100.00 1164955
Iowa 2376.6 541 2376.60 5648227.56 541.00 292681.00 1285740.6
Louisiana 3863.8 1019 3863.80 ########## 1019.00 1038361.00 3937212.2
Massachusetts 1938 225 1938.00 3755844.00 225.00 50625.00 436050
Mississippi 3048.6 803 3048.60 9293961.96 803.00 644809.00 2448025.8
Nebraska 2554.3 371 2554.30 6524448.49 371.00 137641.00 947645.3
New Jersey 1789.6 293 1789.60 3202668.16 293.00 85849.00 524352.8
North Carolina 3109.7 455 3109.70 9670234.09 455.00 207025.00 1414913.5
Oklahoma 3432.7 948 3432.70 ########## 948.00 898704.00 3254199.6
Rhode Island 2137.6 254 2137.60 4569333.76 254.00 64516.00 542950.4
Tennessee 3487 549 3487.00 ########## 549.00 301401.00 1914363
Vermont 1855.7 255 1855.70 3443622.49 255.00 65025.00 473203.5
West Virginia 2405.3 486 2405.30 5785468.09 486.00 236196.00 1168975.8
Total 47102.3 9370 47102.30 ########## 9370.00 6136566.00 28494687.20
Mean 2770.72 551.18 8258402.59 360974.47
SD 786.03 246.48 4564443.54 300186.95
Covariance 1780917.95

Calculate b (formula 12.2, p. 330)
Calculate a (formula 12.3, p. 330)

Find your home state in this Table
https://ucr.fbi.gov/crime-in-the-u.s/2016/crime-in-the-u.s.-2016/topic-pages/tables/table-3

Calculate the Total Crime Rate for that state by adding together Violent Crime Rate per 100,000 inhabitants + Property Crime Rate per 100,000 inhabitants. You will find this information in the last line of data for each state (State Total row). If you are not from the US, pick the state you would most like to visit.

Calculate the predicted incarceration rate for that state (formula 12.1; example on page 332.)

Without knowledge of crime rate, our best estimate for each state would be the overall average. Based on our sample, the Average Incarceration rate is 551.18 per 100,000 inhabitants. By how much, if at all, does using the value predicted by the prediction equation improve your estimation?

Calculate r2 as illustrated on page 338, or using formula 12.6 on page 341.
Calculate r as illustrated on page 345.
Interpret each of these two statistics.