Solve the system of equations and choose the correct answer from the list of options. (4 points)
1 answer:
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Answer:
There where 10 <u>more</u> Small boxes sold than Large boxes.
Step-by-step explanation:
<u>This is a typical question that can be solved by obtaining a system of two linear equations and solving for each variable. </u>
In principle Linear Equations are algebraic expressions denoting a relationship between a Dependent variable and an Independent variable
. In a system of Two Linear equations we have<u> two equations</u> of the same variable sets (thus Two Independent variables) so in this case both
and
will be variable terms.
Now with respect to the question and the given information, here our two Variable terms will be the small and the large boxes.
<u>Given Information:</u>
- Small Boxes (lets call them
) cost $1 per box
- Large Boxes (lets call them
) cost $4 per box
- Total Number of Boxes sold is 30
- Total Profit from sold Boxes is $60
Thus from the above we can obtain one equation denoting the Total Number of Boxes sold and one equation denoting the Total Profit from sold boxes, respectively, as follow:
Eqn(1): Total Number of Boxes
Eqn(2): Total Profit from sold boxes
Now we have a system of two linear equations which we can solve and find the number of small and large boxes, and
respectively.
From Eqn(1) we see that
Eqn(3).
Plugging Eqn(3) in Eqn(2) we can solve for as:
Factored out bracket
Gather similar terms on each side and simplify
Plugging in the value for in Eqn(3) we have
So we know that they were<u> 10 Large Boxes and 20 Small Boxes sold</u>, thus to answer our question, there where 10 more Small boxes sold than Large boxes.
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
The best option for this case would be:
We would switch to α = .01 for a more powerful test.
Step-by-step explanation:
Previous concepts and data given
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".
represent the sample mean
represent the sample standard deviation
n=18 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 is less than 40, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-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".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
First we need to calculate the degrees of freedom given by:
Since is a left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
The best option for this case would be:
We would switch to α = .01 for a more powerful test.
Since the p values is just a little higher than th significance level 0.051>0.05 but the values are two close. If we change the value of the significance by 0.01, we have that 0.051>0.01 and it's a more powerful test.