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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 6 - Problem 21se
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 6 - Problem 21se

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# Two machines are used to package laundry detergent. It is

ISBN: 9780073401331 38

## Solution for problem 21SE Chapter 6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 21SE

Two machines are used to package laundry detergent. It is known that weights of boxes are normally distributed. Four boxes from each machine have their contents carefully weighed, with the following results (in grams):

An engineer wishes to test the null hypothesis that the mean weights of boxes from the two machines are equal. He decides to assume that the population variances are equal, reasoning as follows:

The sample variances are $$s_{1}^{2}=7.00$$ for machine 1 and $$s_{2}^{2}=17.33$$ for machine 2. The F statistic for testing for equality of population variances is $$F_{3,3}=s_{2}^{2} / s_{1}^{2}=2.48$$. The upper 10% point of the $$F_{3,3}$$ distribution is 5.39. Since the null hypothesis specifies that the variances are equal, I determine that the P-value is greater than 2(0.10) = 0.20. Therefore I do not reject the null hypothesis, and I conclude that the variances are equal.

a. Has the F test been done correctly?

b. Is the conclusion justified? Explain.

Equation Transcription:

Text Transcription:

s12=7.00

s22=17.33

F3,3=s22/s12=2.48

F3,3

2(0.10)=0.20

Step-by-Step Solution:
Step 1 of 3

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

Since the solution to 21SE from 6 chapter was answered, more than 342 students have viewed the full step-by-step answer. This full solution covers the following key subjects: variances, equal, null, boxes, hypothesis. 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. The answer to “?Two machines are used to package laundry detergent. It is known that weights of boxes are normally distributed. Four boxes from each machine have their contents carefully weighed, with the following results (in grams): An engineer wishes to test the null hypothesis that the mean weights of boxes from the two machines are equal. He decides to assume that the population variances are equal, reasoning as follows:The sample variances are $$s_{1}^{2}=7.00$$ for machine 1 and $$s_{2}^{2}=17.33$$ for machine 2. The F statistic for testing for equality of population variances is $$F_{3,3}=s_{2}^{2} / s_{1}^{2}=2.48$$. The upper 10% point of the $$F_{3,3}$$ distribution is 5.39. Since the null hypothesis specifies that the variances are equal, I determine that the P-value is greater than 2(0.10) = 0.20. Therefore I do not reject the null hypothesis, and I conclude that the variances are equal.a. Has the F test been done correctly?b. Is the conclusion justified? Explain.________________Equation Transcription:Text Transcription:s12=7.00s22=17.33F3,3=s22/s12=2.48F3,32(0.10)=0.20” is broken down into a number of easy to follow steps, and 154 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 21SE from chapter: 6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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