How many meters in one dekaliter
2 answers:
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Answer:
Null hypothesis:
Alternative hypothesis:
Step-by-step explanation:
1) Previous concepts and data given
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
A right tailed test (sometimes called an upper test) is when the alternative hypothesis statement contains a greater than (>) symbol.
represent the sample mean
s represent the sample standard deviation
n represent the sample selected
significance level
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean for fluorescent bulbs is no more than 3.24 mg of mercury, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
IIf we know the population deviation we can apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
If the product of 2 matrices are I this means that B is inverse matrix of A.
the matrix A has been given
if we put symbols for the numbers in matrix A as shown below;
![\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] ](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%0A)
we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values
D = -1x8 - (4x-3)
= -8 + 12 = 4
to find the inverse we need to exchange a and d and then multiply both b and c by -1
![\left[\begin{array}{ccc}8&-4\\3&-1\\\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-4%5C%5C3%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20)
and then have to divide all the terms in matrix by determinant (4)
![\left[\begin{array}{ccc} \frac{8}{4} & \frac{-4}{4} \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cfrac%7B8%7D%7B4%7D%20%26%20%5Cfrac%7B-4%7D%7B4%7D%20%5C%5C%20%20%5Cfrac%7B3%7D%7B4%7D%20%26%20%5Cfrac%7B-1%7D%7B4%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
the simplified inverse matrix B is;
![\left[\begin{array}{ccc} 2 & -1 \\ \frac{3}{4} & \frac{-1}{4} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%202%20%26%20-1%20%5C%5C%20%5Cfrac%7B3%7D%7B4%7D%20%26%20%5Cfrac%7B-1%7D%7B4%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
the matrix A has been given
if we put symbols for the numbers in matrix A as shown below;
we need to first find the determinant (D)
D = ad - bc
where a = -1 , b = 4, c = -3 and d = 8
substituting these values
D = -1x8 - (4x-3)
= -8 + 12 = 4
to find the inverse we need to exchange a and d and then multiply both b and c by -1
and then have to divide all the terms in matrix by determinant (4)
the simplified inverse matrix B is;