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In the article "Groundwater Electromagnetic Imaging in

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 11SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 11SE

Problem 11SE

In the article "Groundwater Electromagnetic Imaging in Complex Geological and Topographical Regions: A Case Study of a Tectonic Boundary in the French Alps" (S. Houtot, P. Tarits, et al. Geophysics, 2002:1048-1060), the pH was measured for several water samples in various locations near Gittaz Lake in the French Alps. The results for 11 locations on the northern side of the lake and for 6 locations on the southern side are as follows:

Northern side:

 

  8.1

  8.2

  8.1

 8.2

 8.2

 7.4

  7.3

7.4

8.1

 8.1

 7.9

 

Southern side:

 7.8

8.2

7.9

7.9

 8.1

8.1

Find a 98% confidence interval for the difference in pH between the northern and southern side.

Step-by-Step Solution:

Answer:

Step 1 of 1:

In this question, we are asked to find a 98% confidence interval for the difference in between the northern and southern side.

The results for 11 locations on the northern side of the lake and for 6 locations on the southern side are given below on the table:

Northern side:

 

  8.1

  8.2

  8.1

 8.2

 8.2

 7.4

  7.3

7.4

8.1

 8.1

 7.9

 

Southern side:

 7.8

8.2

7.9

7.9

 8.1

8.1

Let be a small sample of size from a population with mean , let  be a small sample of size from a population with mean, then a level  confidence interval for difference between population mean is

……….(1)

Has an approximate Student’s  distribution.

The number of degrees of freedom to use for this distribution is given by

……….(2)

Let be a sample. The sample mean is

……….(3)

Let be a sample. The sample variance is

……….(4)

Use equation (3) and (4) to calculate the sample mean and sample standard deviation.

Let be a sample taken on 11 locations on the northern side of the lake.

Let be a sample taken on 6 locations on the southern side of the lake.

Hence,

sample mean

Sample variance

sample mean

Sample variance

Using above value, calculate the degrees of freedom,

 =

 (rounded down to nearest integer)

So the confidence interval is using equation (1),

= 0.091 0.3279

Hence a 98% confidence interval for the difference in between the northern and southern side is


Step 2 of 1

Chapter 5, Problem 11SE is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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