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Based on a large sample of capacitors of a certain type, a

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

Solution for problem 21E Chapter 5.1

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 21E

Based on a large sample of capacitors of a certain type, a 95% confidence interval for the mean capacitance, in µF, was computed to be (0.213,0.241). Find a 90% confidence interval for the mean capacitance of this type of capacitor

Step-by-Step Solution:

Step 1 of 3:

Based on a large sample  of capacitors of a certain type, the 95% CI for the mean capacitance is (0.213,0.241). We have to find the 90% CI for the mean capacitance of the same type  of capacitor.

Step 2 of 3:

 To find the 95% confidence interval for the  mean capacitance,

     set      t = .95

           

            1- t  = 0.05

           

             =  0.025

We have to find the Z-score , = .

We can find  from the normal table (area under normal curve). The value 0.975 falls in the row 1.9 under column 0.06.

                            

So the 95% CI for the mean capacitance is

                                     

If the population mean and variance is unknown then we can estimate the CI as

                                      ……. (1)

Similarly in order to find the 90% CI for the mean capacitance,

     set      t = .90

           

            1- t  = 0.1

           

             =  0.05

We have to find the Z-score , = .

We can find  from the normal table (area under normal curve). The value 0.95 falls in the row 1.6 under column 0.04.

                            

   

               So the 90% CI for the mean capacitance is

                                       

The estimate of the CI will be

                                        …….. (2)

Step 3 of 3

Chapter 5.1, Problem 21E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Since the solution to 21E from 5.1 chapter was answered, more than 383 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 21E from chapter: 5.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “Based on a large sample of capacitors of a certain type, a 95% confidence interval for the mean capacitance, in µF, was computed to be (0.213,0.241). Find a 90% confidence interval for the mean capacitance of this type of capacitor” is broken down into a number of easy to follow steps, and 40 words. This full solution covers the following key subjects: type, capacitance, mean, interval, confidence. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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