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.

Question

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 14, Problem 14.1.8RE

To determine

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.

Expert Solution & Answer

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 14, Problem 14.1.8RE

To determine

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.

Expert Solution & Answer

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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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Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 14, Problem 14.1.8RE

To determine

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.

Expert Solution & Answer

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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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Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 14, Problem 14.1.8RE

To determine

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.

Expert Solution & Answer

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 14, Problem 14.1.8RE

To determine

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.

Expert Solution & Answer

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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.

Answer 6

Chapter 14, Problem 14.1.8RE

To determine

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.

Expert Solution & Answer

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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.

Answer 7

Chapter 14, Problem 14.1.8RE

To determine

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 8

Expert Solution & Answer

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.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

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.

Range=highest value−lowest value=9.8−2.9=6.9

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 2^nd cluster as a sample.

To calculate means for unemployment rates and mean of average weekly benefits for the selected 2^nd 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,

sample mean of unemployment rates =Sum of the samples of unemployment ratesNumber of samples in unemployment rate=49.510=4.95

The population mean of unemployment is,

Mean of unemployment rates= 6.5+6.5+8.0+7.5+8.9+6.8+7.8+........+6.7+4.650= 336.450= 6.728

The sample mean of average weekly benfit is,

Sample mean of average weekly benfit =Sum of the samples average weekly benefitsNumber of samples in weekly average benefits =3,36110 =336.1

The population mean of average weekly benefits is,

Mean of average weekly benefits=( 207+250+221+289+301+356+345+...+275+276+359)50= 15,12250= 302.44

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.

Answer 12

Ch. 14.1 - The White or Wheat Bread Debate Read the following...Ch. 14.1 - Name the four basic sampling techniques.Ch. 14.1 - Why are samples used in statistics?Ch. 14.1 - What is the basic requirement for a sample?Ch. 14.1 - Why should random numbers be used when you are...Ch. 14.1 - List three incorrect methods that are often used...Ch. 14.1 - What is the principle behind random numbers?Ch. 14.1 - List the advantages and disadvantages of random...Ch. 14.1 - List the advantages and disadvantages of...Ch. 14.1 - List the advantages and disadvantages of...

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.

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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

Explanation of Solution

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Chapter 14 Solutions