
The
To compare: The sample mean with the U.S. figures.

Answer to Problem 14.1.8RE
Mean of unemployment rates is 4.95, and mean of the average weekly benefits is 336.1
By comparing the result with the U.S. figures, it is clear that the there is large difference between the sample of the unemployment rate and the population unemployment rate. And also that the there is large difference between the sample of the weekly benefits and the population of weekly benefits.
Explanation of Solution
Given info:
The unemployment rate and average weekly benefit for all the states in U.S. are provided.
Calculation:
Answers will vary. One of the possible answers is given below:
There are many ways to divide the population into clusters. Here the population is divided into cluster based on ranges of unemployment rates.
- Procedure for selecting the 10 samples by using cluster sampling is as follows.
- In the data the highest unemployment rate is 9.8 and least unemployment rate is 2.9.
- Divide the data into 5 clusters, based on the range of unemployment rates.
- The range obtained is 6.9. Divide the range by 5, to get 1.38.
- Arrangement ofintervals with range 1.38 as follows.
2.9-4.28 |
4.29-5.66 |
5.67-7.04 |
7.05-8.42 |
8.42-9.8 |
- Arrange all the values of unemployment rates according to the intervals and each interval is named as cluster1, cluster2, cluster3, cluster4, cluster5.
- The following table represents the 5 clusters, which are arranged according to the intervals.
Cluster1:
State | Unemployment rates | Weekly average benefits |
NE | 3.9 | 276 |
ND | 2.9 | 396 |
SD | 3.8 | 276 |
Cluster2:
State | Unemployment rates | Weekly average benefits |
HI | 4.8 | 424 |
IA | 4.6 | 337 |
KS | 5.4 | 341 |
MN | 5.1 | 367 |
NH | 5.3 | 287 |
OK | 5.4 | 293 |
UT | 4.4 | 345 |
VT | 4.4 | 313 |
VA | 5.5 | 295 |
WY | 4.6 | 359 |
Cluster3:
States | Unemployment rates | Weekly average benefits |
AL | 6.5 | 207 |
AK | 6.5 | 250 |
CO | 6.8 | 256 |
DE | 6.7 | 245 |
ID | 6.2 | 246 |
LA | 6.2 | 207 |
ME | 6.7 | 285 |
MD | 6.6 | 329 |
MO | 6.5 | 242 |
MT | 5.6 | 290 |
NM | 6.9 | 303 |
TX | 6.3 | 241 |
WA | 7.0 | 387 |
WV | 6.5 | 275 |
WI | 6.7 | 276 |
Cluster4:
States | Unemployment rates | Weekly average benefits |
AZ | 8.0 | 221 |
AR | 7.5 | 289 |
CT | 7.8 | 348 |
FL | 7.2 | 231 |
GA | 8.2 | 267 |
IN | 7.5 | 243 |
MA | 7.1 | 424 |
KY | 8.3 | 292 |
NJ | 8.2 | 398 |
NY | 7.7 | 308 |
NC | 8.0 | 290 |
OH | 7.4 | 318 |
OR | 7.7 | 316 |
PA | 7.4 | 360 |
SC | 7.6 | 248 |
TN | 8.2 | 235 |
Cluster 5:
states | Unemployment rates | Average weekly benefits |
CA | 8.9 | 301 |
IL | 9.2 | 324 |
MI | 8.8 | 293 |
MS | 8.6 | 194 |
NV | 9.8 | 308 |
RI | 9.5 | 351 |
- From the above clusters select the 2nd cluster as a sample.
To calculate means for unemployment rates and mean of average weekly benefits for the selected 2nd cluster.
Cluster2:
State | Unemployment rates | Weekly average benefits |
HI | 4.8 | 424 |
IA | 4.6 | 337 |
KS | 5.4 | 341 |
MN | 5.1 | 367 |
NH | 5.3 | 287 |
OK | 5.4 | 293 |
UT | 4.4 | 345 |
VT | 4.4 | 313 |
VA | 5.5 | 295 |
WY | 4.6 | 359 |
The sample mean of unemployment is,
The population mean of unemployment is,
The sample mean of average weekly benfit is,
The population mean of average weekly benefits is,
Comparisons of means:
The sample mean of unemployment rates is 4.95, and the population mean of unemployment rates is 6.728. That implies that the sample mean is lesser than the population mean. It is clear that there is larger difference between the sample mean and the population mean.
Also, the sample mean of the average weekly benefits is 336.1, and the population mean of pupils per teacher is 302.44. That implies that the sample mean is greater than the population mean. It is clear that there is larger difference between the sample mean and the population mean.
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Chapter 14 Solutions
Loose Leaf for Elementary Statistics: A Step By Step Approach
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