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Statistics / Probability and Statistics for Engineering and the Sciences 9 / Chapter 8 / Problem 19E

Probability and Statistics for Engineering and the Sciences | 9th Edition | ISBN: 9781305251809 | Authors: Jay L. Devore

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Chapter 8, Problem 19E

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QUESTION:

The melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in \(\bar{x}\)=94.32. Assume that the distribution of the melting point is normal with σ = 1.20.

a. Test H0: \(\mu\) = 95 versus Ha: m \(\neq\) 95 using a two tailed level .01 test.

b. If a level .01 test is used, what is b(94), the probability of a type II error when \(\mu\) = 94?

c. What value of n is necessary to ensure that \(\beta\)(94) = .1 when a = .01?

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QUESTION:

The melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in \(\bar{x}\)=94.32. Assume that the distribution of the melting point is normal with σ = 1.20.

a. Test H0: \(\mu\) = 95 versus Ha: m \(\neq\) 95 using a two tailed level .01 test.

b. If a level .01 test is used, what is b(94), the probability of a type II error when \(\mu\) = 94?

c. What value of n is necessary to ensure that \(\beta\)(94) = .1 when a = .01?

ANSWER:

Step 1 of 5

Given that,

The sample size is 16, the sample mean and .

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