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# Refer to Exercise 8.a. Find a 99% upper confidence bound ISBN: 9780073401331 38

## Solution for problem 15E Chapter 5.1

Statistics for Engineers and Scientists | 4th Edition

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Problem 15E

Refer to Exercise 8.

a. Find a 99% upper confidence bound for the mean temperature.

b. The claim is made that the mean temperature is less than 349.5°F. With what level of confidence can this statement be made?

Exercise 8

Oven thermostats were tested by setting them to 350°F and measuring the actual temperature of the oven. In a sample of 67 thermostats, the average temperature was 348.2°F and the standard deviation was 5.1°F.

a. Find a 90% confidence interval for the mean oven temperature.

b. Find a 95% confidence interval for the mean oven temperature.

c. What is the confidence level of the interval (347.5, 348.9)?

d. How many thermostats must be sampled so that a 90% confidence interval specifies the mean to within ±0.8°F?

e. How many thermostats must be sampled so that a 95% confidence interval specifies the mean to within ±0.8°F?

Step-by-Step Solution:
Step 1 of 3

Solution 15E

Step1 of 3:

Let us consider a random variable X it represents the oven temperature. Here random variable X follows normal distribution with mean standard deviation and n = 67.

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 a 99% upper confidence bound for the mean temperature.

b). We need to find level of confidence can this statement be made by taking the mean temperature is less than 349.5°F.

Step2 of 3:

a).

Here we have to find 99%  CI, let us take .

Now,  = 0.01

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

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

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