The sodium content of twenty 300-gram boxes of organic cornflakes was determined. The data (in milligrams) are as follows: 131.23 130.67 130.91 129.54 129.64 128.77 130.72 128.33 128.24 129.65 130.14 129.29 128.71 129.00 129.39 130.42 129.53 130.12 129.78 130.92 (a) Test the hypothesis Ho: μ = 130 versus H₁: 130. Use a = 0.05. Ho- (b) Find the best lower-bound and upper-bound for the P-value for this test. < P-value < (c) Approximate the power of the test if the true mean sodium content is 130.5 milligrams. The power of the test is (d) Approximately what sample size would be required to detect a true mean sodium content of 130.1 milligrams if we wanted the power of the test to be at least 0.75? (Give the highest possible boundary for n.) n>
The sodium content of twenty 300-gram boxes of organic cornflakes was determined. The data (in milligrams) are as follows: 131.23 130.67 130.91 129.54 129.64 128.77 130.72 128.33 128.24 129.65 130.14 129.29 128.71 129.00 129.39 130.42 129.53 130.12 129.78 130.92 (a) Test the hypothesis Ho: μ = 130 versus H₁: 130. Use a = 0.05. Ho- (b) Find the best lower-bound and upper-bound for the P-value for this test. < P-value < (c) Approximate the power of the test if the true mean sodium content is 130.5 milligrams. The power of the test is (d) Approximately what sample size would be required to detect a true mean sodium content of 130.1 milligrams if we wanted the power of the test to be at least 0.75? (Give the highest possible boundary for n.) n>
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![The sodium content of twenty 300-gram boxes of organic cornflakes was determined. The data (in milligrams) are as follows:
131.23, 130.67, 130.91, 129.54, 129.64
128.77, 130.72, 128.33, 128.24, 129.65
130.14, 129.29, 128.71, 129.00, 129.39
130.42, 129.53, 130.12, 129.78, 130.92
(a) Test the hypothesis \( H_0 : \mu = 130 \) versus \( H_1 : \mu \neq 130 \). Use \( \alpha = 0.05 \).
\[ H_0 : \]
(b) Find the best lower-bound and upper-bound for the P-value for this test.
\[ \text{< P-value <} \]
(c) Approximate the power of the test if the true mean sodium content is 130.5 milligrams.
The power of the test is \[ \text{ } \].
(d) Approximately what sample size would be required to detect a true mean sodium content of 130.1 milligrams if we wanted the power of the test to be at least 0.75?
\[ n > \] (Give the highest possible boundary for n.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbba0909-7b4f-4e80-8e24-06dfda2d061e%2F4df940bd-723e-40d6-ba9b-78081f44ecec%2Fh1mtguu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The sodium content of twenty 300-gram boxes of organic cornflakes was determined. The data (in milligrams) are as follows:
131.23, 130.67, 130.91, 129.54, 129.64
128.77, 130.72, 128.33, 128.24, 129.65
130.14, 129.29, 128.71, 129.00, 129.39
130.42, 129.53, 130.12, 129.78, 130.92
(a) Test the hypothesis \( H_0 : \mu = 130 \) versus \( H_1 : \mu \neq 130 \). Use \( \alpha = 0.05 \).
\[ H_0 : \]
(b) Find the best lower-bound and upper-bound for the P-value for this test.
\[ \text{< P-value <} \]
(c) Approximate the power of the test if the true mean sodium content is 130.5 milligrams.
The power of the test is \[ \text{ } \].
(d) Approximately what sample size would be required to detect a true mean sodium content of 130.1 milligrams if we wanted the power of the test to be at least 0.75?
\[ n > \] (Give the highest possible boundary for n.)
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