The mean of unemployment rates by using cluster sampling and the mean of average weekly benefits by using cluster sampling.
To compare: The sample mean with the U.S. figures.
Answer to Problem 14.1.8RE
Mean of unemployment rates is 8.29, and mean of the average weekly benefits is 301.8.
By comparing the result with the U.S. figures, it is clear that there is slight difference between the cluster sample mean and the U.S. figures of unemployment rates and the cluster sample mean and the U.S. figures are very close or approximately equal in values in case of weekly average 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 to ensure maximum heterogeneity within each cluster. Here, the population is divided into 5 clusters of 10 states each, alphabetically. Heterogeneity is preserved in existing alphabetical arrangement of data.
Procedure for selecting the 10 samples by using cluster sampling is as follows.
- Take the 1st 10 states as Cluster1,
- Take the 2nd set of 10 states as Cluster2,
- Take the 3rd set of 10 states as Cluster,
- Take the 4th set of 10 states as Cluster4 and
- Take the 5th set of 10 states as Cluster5
Cluster1:
States | AL | AK | AZ | AR | CA | CO | CT | DE | FL | GA |
Cluster2:
States | HI | ID | IL | IN | IA | KS | KY | LA | ME | MD |
Cluster3:
States | MA | MI | MN | MS | MO | MT | NE | NV | NH | NJ |
Cluster4:
States | NM | NY | NC | ND | OH | OK | OR | PA | RI | SC |
Cluster5:
States | SD | TN | TX | UT | VT | VA | WA | WV | WI | WY |
- From the figure 14.1(Table of random numbers), select a starting point for randomly selecting a cluster.
- Here, the selected starting point is ‘2’ which is present in sixth row and first column.
- Thus, the randomly chosen cluster is Cluster2.
To calculate means for unemployment rates and mean of average weekly benefits for the selected Cluster2.
Cluster2:
State | Unemployment rates | Weekly average benefits |
HI | 6.6 | 416 |
ID | 9.3 | 255 |
IL | 10.3 | 317 |
IN | 10.2 | 295 |
IA | 6.1 | 321 |
KS | 7.0 | 326 |
KY | 10.5 | 289 |
LA | 7.5 | 209 |
ME | 7.9 | 274 |
MD | 7.5 | 316 |
The sample mean of unemployment rate is,
The U.S. figure for unemployment rate is 9.6.
The sample mean of average weekly benefit is,
The U.S. figure for average weekly benefits is 299.
Comparisons of means:
The sample mean of unemployment rates is 8.29, and the U.S. figure for unemployment rate is 9.6. That implies that the sample mean is slightly lesser than the population mean. It is clear that there is slight difference between the sample mean and the U.S. figures.
Again, the sample mean of the average weekly benefits is 301.8, and the U.S. figure for average weekly benefits is 299. It is clear that the sample mean and the U.S. figures are very close or approximately equal in values.
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Chapter 14 Solutions
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