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The temperature of a certain solution is estimated by

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

Problem 17SE 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 17SE

The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The estimate is 37°C, and the uncertainty (standard deviation) in this estimate is 0.1°C.

a. Find a 95% confidence interval for the temperature.

b. What is the confidence level of the interval 37 ± 0.1°C?

c. If only a small number of independent measurements had been made, what additional assumption would be necessary in order to compute a confidence interval?

d. Making the additional assumption, compute a 95% confidence interval for the temperature if 10 measurements were made.

Step-by-Step Solution:

Answer:

Step 1 of 4:

(a)

In this question, we are asked to find a  confidence interval for the temperature.

Given the temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them.

The estimate is , and the uncertainty (standard deviation) in this estimate is .

Hence our sample mean  is and standard deviation  

Since the large number of independent measurements has been taken, then a level  confidence interval for temperature is,

 ………(1)

we want 95% confidence interval, then a level is

 

 

 and

Then for  is , hence

A 95% confidence interval for temperature is,

 Hence the 95% confidence interval for temperature is (36.804, 37.196).

Step 2 of 4:

(b)

In this question, we are asked to find the confidence level of the interval .

We know the confidence level of the interval can be written like this,

…………..(2)

We have given the interval,

 ………..(3)

Compare equation (2) and (3), we have,

Using the , the area to the left of is approximately .

Therefore , so the level is,

 or approximately .

Hence the confidence level of the interval  is 68%.

Step 3 of 4

Chapter 5, Problem 17SE is Solved
Step 4 of 4

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

This full solution covers the following key subjects: confidence, interval, temperature, measurements, additional. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 17SE from 5 chapter was answered, more than 292 students have viewed the full step-by-step answer. The answer to “The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The estimate is 37°C, and the uncertainty (standard deviation) in this estimate is 0.1°C.a. Find a 95% confidence interval for the temperature.________________b. What is the confidence level of the interval 37 ± 0.1°C?________________c. If only a small number of independent measurements had been made, what additional assumption would be necessary in order to compute a confidence interval?________________d. Making the additional assumption, compute a 95% confidence interval for the temperature if 10 measurements were made.” is broken down into a number of easy to follow steps, and 93 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 17SE from chapter: 5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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