A triangle has one angle that is three times the size of another, and a third angle that is 16degrees smaller than the larger of
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"<span>Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = (x - y), find 
, 
, the t-test statistic, and the critical values to test the claim that 
"
You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.
For the example, please refer to the attached picture.
A) Find </span><span>
You are asked to find the mean difference between the two variables, which is given by the formula:
These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)
In our example:
</span><span>
</span>
B) Find <span>
</span><span>You are asked to find the standard deviation, which is given by the formula:
</span>
These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1
In our example:
= √14.5
= 3.81
C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
where SE = standard error is given by the formula:
These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract
6) divide by the standard error
In our example:
SE = 3.81 / √8
= 1.346
The problem gives us <span>, therefore:
t = [(9.75 - 9) - 0] / 1.346</span>
= 0.56
D) Find
You are asked to find what is the t-value for a 0.05 significance level.
In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).
We find <span>
</span>
Since our t-value is less than <span>
</span> we can reject our null hypothesis!!
You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.
For the example, please refer to the attached picture.
A) Find </span><span>
You are asked to find the mean difference between the two variables, which is given by the formula:
These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)
In our example:
</span><span>
B) Find <span>
</span><span>You are asked to find the standard deviation, which is given by the formula:
</span>
These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1
In our example:
= √14.5
= 3.81
C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
where SE = standard error is given by the formula:
These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract
6) divide by the standard error
In our example:
SE = 3.81 / √8
= 1.346
The problem gives us <span>
t = [(9.75 - 9) - 0] / 1.346</span>
= 0.56
D) Find
You are asked to find what is the t-value for a 0.05 significance level.
In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).
We find <span>
Since our t-value is less than <span>
Answer:
Step-by-step explanation:
By putting the numbers in the given equation,
2x + 3 + 3x = 7x + 9
5x + 3 = 7x + 9
(5x + 3) - 7x = (7x + 9) - 7x
(5x - 7x) + 3 = 9
-2x + 3 = 9
(-2x + 3) - 3 = 9 - 3
-2x = 6
-x = 3
x = -3
Therefore, our equation is correct which has a negative result.
In place of 6 if we use 8, value of x will be negative again.