The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95 % confident interval for the mean level of each pollutant for the year 2.

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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 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

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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 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

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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 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

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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 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

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Answer 5

Chapter 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Answer 6

Chapter 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Answer 7

Chapter 8, Problem 4CS

To determine

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Answer 8

Expert Solution & Answer

Answer to Problem 4CS

The box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given information:

The number of pollutants is 4 and the data is shown in table below.

Year 1				Year 2
PM	OC	TC	LE	PM	OC	TC	LE
21.7	15.6	17.73	1.78	27.0	15.79	19.46	2.06
27.8	15.6	17.87	2.25	24.7	13.61	15.98	3.10
24.7	17.2	18.75	1.98	21.8	12.94	15.79	2.68
15.3	8.3	9.21	0.67	23.2	12.97	16.32	2.80
18.4	11.3	12.46	0.86	23.3	I l.19	13.49	2.07
14.4	8.4	9.66	1.93	16.2	9.61	12.44	2.14
19.0	13.2	14.73	1.51	13.4	6.97	8.40	2.32
23.7	1 1.4	13.23	1.98	13.0	7.96	10.02	2. 18
22.4	13.8	17.08	1.69	16.9	8.43	11.08	2.06
25.6	13.2	15.86	2.30	26.3	14.92	21.46	1.94
15.0	15.7	17.27	1.24	31.4	17.15	20.57	1.85
17.0	9.3	10.2 1	1.44	40. l	15.13	19.64	2. 1 1
23.2	10.5	11.47	1.43	28.0	8.66	10.75	2.50
17.7	14.2	15.64	1.07	4.2	15.95	20.36	2.27
11.l	11.6	13.48	0.59	15.9	11.73	14.59	2.17
29.8	7.0	7.795	2.10	20.5	14.34	17.64	2.74
20.0	19.9	21.20	1.73	23.8	8.99	1 1.75	2.45
21.6	14.8	15.65	1.56	14.6	10.63	13.12
14.8	12.6	13.51	1.1	17.8
21.0	9.1	9.94

Concept used:

MINITAB is used.

Calculation:

The procedure for box-plot is, choose graph then box-plot, under the multiple Y’s choose simple and click ok.

In graph variables, enter the data of PM, OC, TC and LE and click ok.

The Box-plot is shown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 1

Figure-1

From Figure-1, there is no sign of strong skews and no outliers.

The 95% confident interval for the mean level of PM pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 2

Figure-2

The 95% confident interval for the mean level of PM pollutant for year 2 is (17.33,25) .

The 95% confident interval for the mean level of OC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 3

Figure-3

The 95% confident interval for the mean level of OC pollutant for year 2 is (10.493,13.615) .

The 95% confident interval for the mean level of TC pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 4

Figure-4

The 95% confident interval for the mean level of TC pollutant for year 2 is (13.149,17.169) .

The 95% confident interval for the mean level of LE pollutant for year 2 is sown below.

ELEMENTARY STATISTICS-ALEKS ACCESS CODE, Chapter 8, Problem 4CS , additional homework tip 5

Figure-5

The 95% confident interval for the mean level of LE pollutant for year 2 is (2.144,2.496) .

Therefore, the box-plot for the four pollutants is shown in Figure-1 and assumptions for constructing a confidence interval are satisfied and 95% confident interval for the mean level of each pollutant for the year 2 is (17.33,25),(10.493,13.615),(13.149,17.169) and (2.144,2.496) .

Answer 12

The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95 % confident interval for the mean level of each pollutant for the year 2.

Videos

To find: The box-plot for the four pollutants to verify that the assumptions for constructing a confidence interval are satisfied and the 95% confident interval for the mean level of each pollutant for the year 2.

Answer to Problem 4CS

Explanation of Solution

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