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The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO, in a sample is normally distributed with o = 0.32 and that x = 5.22. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: H = 5.5 H: u< 5.5 O Ho: H = 5.5 H: u2 5.5 O Ho: H = 5.5 Hg: H # 5.5 O Ho: H = 5.5 H: 4 > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = -3,50 P-value = 0.0004 State the conclusion in the problem context. O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. OReject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is u = 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H.? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and B(5.6) = 0.01? (Round your answer up to the next whole number.) n = samples

The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO, in a sample is normally distributed with o = 0.32 and that x = 5.22. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: H = 5.5 H: u< 5.5 O Ho: H = 5.5 H: u2 5.5 O Ho: H = 5.5 Hg: H # 5.5 O Ho: H = 5.5 H: 4 > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = -3,50 P-value = 0.0004 State the conclusion in the problem context. O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. OReject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is u = 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H.? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and B(5.6) = 0.01? (Round your answer up to the next whole number.) n = samples

MATLAB: An Introduction with Applications
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 desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of Sio, in a sample is normally distributed with o = 0.32 and that x = 5.22. (Use a = :0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. О н: и 3 5.5 Hai H < 5.5 O Ho: µ = 5.5 Ha: u 2 5.5 Ho: H = 5.5 Hai H + 5.5 Ο H μ 5.5 Hai H> 5.5 H.: Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = |-3.50 P-value = 0.0004 State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is u 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and ßB(5.6) = 0.01? (Round your answer up to the next whole number.) n = samples
Transcribed Image Text:The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of Sio, in a sample is normally distributed with o = 0.32 and that x = 5.22. (Use a = :0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. О н: и 3 5.5 Hai H < 5.5 O Ho: µ = 5.5 Ha: u 2 5.5 Ho: H = 5.5 Hai H + 5.5 Ο H μ 5.5 Hai H> 5.5 H.: Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = |-3.50 P-value = 0.0004 State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is u 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and ßB(5.6) = 0.01? (Round your answer up to the next whole number.) n = samples
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