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# The temperature of a certain solution is estimated by ## Problem 17SE Chapter 5

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:

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

Step 4 of 4

##### ISBN: 9780073401331

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The temperature of a certain solution is estimated by

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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5 - Problem 17se

Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5 - Problem 17se