The desired percentage of SiO₂ 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 SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.21. (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. Ho: μ = 5.5 H₂: = 5.5 O Ho: μ = 5.5 H₂:μ< 5.5 OH: = 5.5 H₂:25.5 O Ho: H = 5.5 H₂:μ> 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 = P-value= State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. 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 not sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is μ = 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from Ho? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and ß(5.6) = 0.01? (Round your answer up to the next whole number.) n = samples
The desired percentage of SiO₂ 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 SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.21. (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. Ho: μ = 5.5 H₂: = 5.5 O Ho: μ = 5.5 H₂:μ< 5.5 OH: = 5.5 H₂:25.5 O Ho: H = 5.5 H₂:μ> 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 = P-value= State the conclusion in the problem context. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. 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 not sufficient evidence to conclude that the true average percentage differs from the desired percentage. (b) If the true average percentage is μ = 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from Ho? (Round your answer to four decimal places.) (c) What value of n is required to satisfy a = 0.01 and ß(5.6) = 0.01? (Round your answer up to the next whole number.) n = samples
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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Transcribed Image Text:The desired percentage of SiO₂ 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 SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.21. (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.
ⒸHO: μ = 5.5
H₂: μ = 5.5
O Ho: μ = 5.5
H₂:μ< 5.5
Ο Ηγ: μ = 5.5
Η: με 5.5
O Ho: μ = 5.5
H₂:μ> 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 =
P-value =
State the conclusion in the problem context.
O Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.
O Reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage.
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 not sufficient evidence to conclude that the true average percentage differs from the desired percentage.
(b) If the true average percentage is μ = 5.6 and a level α = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from Ho? (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
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