The metric system is based on the number ___. 1 2 10 12
2 answers:
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Given:
A diagram of a circle O, .
To find:
The measure of arc DC.
Solution:
According to the angle of intersecting chords theorem:
Angle at intersection of chords = Half of the sum of intercepted arcs.
Let be the angle between the intersection of chords AC and BD.
(Linear pair)
Using the angle of intersecting chords theorem, we get
On simplification, we get
Divide both sides by 2.
Now,
Therefore, the correct option is C.
Given that t<span>he
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 σ = 0.32 and that 
.
</span>
<span>To investigate whether this indicate conclusively that the true average percentage differs from 5.5.
Part A:
From the question, it is claimed that </span><span>t<span>he desired average percentage of sio2 in a certain type of aluminous cement is 5.5</span></span> and we want to test whether the information from the random sample <span>indicate conclusively that the true average percentage differs from 5.5.
Therefore, the null hypothesis and the alternative hypothesis is given by:
Part B:
The test statistics is given by:
Part C:
The p-value is given by
Part D:
Because the p-value is less than the significant level α, we reject the null hypothesis and conclude that "</span><span>There is sufficient evidence to conclude that the true average percentage differs from the desired percentage."
Part E:
</span>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 H0? (Round your answer to four decimal places.)
The probability of detecting the departure from
is given by
Part F:
What value of n is required to satisfy α = 0.01 and β(5.6) = 0.01? (Round your answer up to the next whole number.)
The value of n is required to satisfy α = 0.01 and β(5.6) = 0.01 is given by
![n=\left[ \frac{\sigma(z_{0.005}+z_{0.01})}{\mu_0-\mu} \right]^2 \\ \\ = \left[\frac{0.32(-2.576-2.326)}{5.5-5.6} \right]^2 \\ \\ =\left[\frac{0.32(-4.902)}{-0.1} \right]^2=\left[\frac{-1.56864}{-0.1} \right]^2 \\ \\ =(15.6864)^2=247](https://tex.z-dn.net/?f=n%3D%5Cleft%5B%20%5Cfrac%7B%5Csigma%28z_%7B0.005%7D%2Bz_%7B0.01%7D%29%7D%7B%5Cmu_0-%5Cmu%7D%20%5Cright%5D%5E2%20%5C%5C%20%20%5C%5C%20%3D%20%5Cleft%5B%5Cfrac%7B0.32%28-2.576-2.326%29%7D%7B5.5-5.6%7D%20%5Cright%5D%5E2%20%5C%5C%20%20%5C%5C%20%3D%5Cleft%5B%5Cfrac%7B0.32%28-4.902%29%7D%7B-0.1%7D%20%5Cright%5D%5E2%3D%5Cleft%5B%5Cfrac%7B-1.56864%7D%7B-0.1%7D%20%5Cright%5D%5E2%20%5C%5C%20%20%5C%5C%20%3D%2815.6864%29%5E2%3D247)
</span>
<span>To investigate whether this indicate conclusively that the true average percentage differs from 5.5.
Part A:
From the question, it is claimed that </span><span>t<span>he desired average percentage of sio2 in a certain type of aluminous cement is 5.5</span></span> and we want to test whether the information from the random sample <span>indicate conclusively that the true average percentage differs from 5.5.
Therefore, the null hypothesis and the alternative hypothesis is given by:
Part B:
The test statistics is given by:
Part C:
The p-value is given by
Part D:
Because the p-value is less than the significant level α, we reject the null hypothesis and conclude that "</span><span>There is sufficient evidence to conclude that the true average percentage differs from the desired percentage."
Part E:
</span>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 H0? (Round your answer to four decimal places.)
The probability of detecting the departure from
Part F:
What value of n is required to satisfy α = 0.01 and β(5.6) = 0.01? (Round your answer up to the next whole number.)
The value of n is required to satisfy α = 0.01 and β(5.6) = 0.01 is given by