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The article “Application of Surgical Navigation to Total

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

Solution for problem 6E 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 6E

The article “Application of Surgical Navigation to Total Hip Arthroplasty” (T. Ecker and S. Murphy, Journal of Engineering in Medicine, 2007:699-712) reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes.

a. Find a 95% confidence interval for the mean surgery time for this procedure.

b. Find a 99.5% confidence interval for the mean surgery time for this procedure.

c. A surgeon claims that the mean surgery time is between 133.9 and 139.9 minutes. With what level of confidence can this statement be made?

d. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes?

e. Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes?

Step-by-Step Solution:
Step 1 of 3

Solution 6E

Step1 of 6:

Let us consider a random variable X it represents the surgery time. Here random variable X follows normal distribution with mean standard deviation and n = 123.

That is

                       

The probability density function of normal distribution is given by

, .

Where,

x = random variable

= mean of X

= variance of X

= standard deviation os X

= mathematical constant and its value is 3.14

Here our goal is:

a).We need to find 95% confidence interval for the mean surgery time for this procedure.

b).We need to find 99.5% confidence interval for the mean surgery time for this procedure.

c).A surgeon claims that the mean surgery time is between 133.9 and 139.9 minutes.We need to check what level of confidence can this statement be made?

d).We need to find  how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes?

e).We need to find how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes?


Step2 of 6:

a).

Here we have to find 95%  CI, let us take .

Now,

 

   = 0.025

Z-scores(are to the right) is given by

                                                                       

  is obtained from standard normal table(area under normal curve). In standard normal table we have to see where 0.9750 value falls, it falls in row 1.9 under column 0.06.

Hence,

Now 95% confidence interval for the mean surgery time for this procedure is given by

     

     

         

(132.9059, 140.8940)

Hence, 95% confidence interval for the mean surgery time for this procedure is

(132.9059, 140.8940).


Step3 of 6:

b).

Here we have to find 99.5%  CI, let us take .

Now,

 

   = 0.0025

Z-scores is given by

                                               

  is obtained from standard normal table(area under normal curve). In standard normal table we have to see where 0.9975 value falls, it falls in row 2.8 under column 0.01.

Hence,

Now 95% confidence interval for the mean surgery time for this procedure is given by

       

     

         

(131.1740, 141.8999)

Hence, 99.5% confidence interval for the mean surgery time for this procedure is

(131.1740, 141.8999).


Step4 of 6:

c).

We have and n = 123.

In a given information we have upper bound 139.9

Now,

 

139.9-136.9 = (2.0377)

                  3 =  (2.0377)

   =

        = 1.4722

Hence, = 1.4722.

Z-scores is given by , and this value is obtained from standard normal table(area under normal curve). In standard normal table we have to see in row 1.4 under column 0.07.

 = 0.9292

Area to the right of Z is  1 - 0.9292

                                      = 0.0708.

Now,

             = 0.1416

Therefore level is (1-) = 1 - 0.1416

                                       = 0.8584.

Hence level is 0.8584.


Step5 of 6:

d).

We know that  (from part (a))

    = 3

= 3

       

         

                     

                           

                              = 218.0150.

Hence, n = 218.0150.


Step6 of 6:

e).

We know that , s = 22.6.

 = 3

= 3

       

         

                     

                           

                              = 374.8354.

Hence, n = 374.8354.


 

 

Step 2 of 3

Chapter 5.1, Problem 6E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “The article “Application of Surgical Navigation to Total Hip Arthroplasty” (T. Ecker and S. Murphy, Journal of Engineering in Medicine, 2007:699-712) reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes.a. Find a 95% confidence interval for the mean surgery time for this procedure.________________b. Find a 99.5% confidence interval for the mean surgery time for this procedure.________________c. A surgeon claims that the mean surgery time is between 133.9 and 139.9 minutes. With what level of confidence can this statement be made?________________d. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes?________________e. Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes?” is broken down into a number of easy to follow steps, and 140 words. Since the solution to 6E from 5.1 chapter was answered, more than 1520 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 6E from chapter: 5.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: mean, minutes, confidence, surgery, interval. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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