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 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 $\left(17.33,25\right),\left(10.493,13.615\right),\left(13.149,17.169\right)$ and $\left(2.144,2.496\right)$ .

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.

  

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.

  

Figure-2

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

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

  

Figure-3

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

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

  

Figure-4

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

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

  

Figure-5

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

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 $\left(17.33,25\right),\left(10.493,13.615\right),\left(13.149,17.169\right)$ and $\left(2.144,2.496\right)$ .