It took a plane 2 hours to go from Dallas to NY with the head wind and 1.5 hours to get back with the tail wind. If the speed of
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>= means greater than or equal to
<= means less than or equal to
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Part A
The graph of y >= -3x+3 will have a solid boundary line and the shading will be above the boundary line.
The boundary line y = -3x+3 has a negative slope so it moves down as you read it from left to right. It goes through the points (0,3) and (1,0)
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The graph of y < (3/2)x - 6 will have a dashed or dotted boundary line. The shading is below the boundary.
The graph y = (3/2)x-6 goes through the two points (0,-6) and (2,-3)
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If you graph both y >= -3x+3 and y < (3/2)x - 6 together, you get what you see in the attached image. This solution shaded region is the result of the overlapping prior shaded regions.
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Part B
Plug (x,y) = (-6,3) into each inequality to see if we get a true inequality or not
For the first inequality we have
y >= -3x+3
3 >= -3*(-6)+3
3 >= 18+3
3 >= 21
which is false. The value 3 is not larger or equal to 21. So right off the bat we know that (-6,3) is NOT a solution. It is NOT in the solution region.
Let's check the other inequality just for the sake of completeness
y < (3/2)x - 6
3 < (3/2)*(-6) - 6
3 < -9 - 6
3 < -15
this is also false. The value -15 is smaller than 3, since it is to the left of 3
We're given more evidence that (-6,3) is NOT in the solution area. It is outside of both shaded areas.
<= means less than or equal to
---------------------------------------------
Part A
The graph of y >= -3x+3 will have a solid boundary line and the shading will be above the boundary line.
The boundary line y = -3x+3 has a negative slope so it moves down as you read it from left to right. It goes through the points (0,3) and (1,0)
--------------
The graph of y < (3/2)x - 6 will have a dashed or dotted boundary line. The shading is below the boundary.
The graph y = (3/2)x-6 goes through the two points (0,-6) and (2,-3)
--------------
If you graph both y >= -3x+3 and y < (3/2)x - 6 together, you get what you see in the attached image. This solution shaded region is the result of the overlapping prior shaded regions.
---------------------------------------------
Part B
Plug (x,y) = (-6,3) into each inequality to see if we get a true inequality or not
For the first inequality we have
y >= -3x+3
3 >= -3*(-6)+3
3 >= 18+3
3 >= 21
which is false. The value 3 is not larger or equal to 21. So right off the bat we know that (-6,3) is NOT a solution. It is NOT in the solution region.
Let's check the other inequality just for the sake of completeness
y < (3/2)x - 6
3 < (3/2)*(-6) - 6
3 < -9 - 6
3 < -15
this is also false. The value -15 is smaller than 3, since it is to the left of 3
We're given more evidence that (-6,3) is NOT in the solution area. It is outside of both shaded areas.
Answer:
1) H0: There is independence between the marital status and the diagnostic of alcoholic
H1: There is association between the marital status and the diagnostic of alcoholic
2) The statistic to check the hypothesis is given by:
3)
4)
And we can calculate the p value given by:
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(19.72,2,TRUE)"
Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.
Step-by-step explanation:
A chi-square goodness of fit test "determines if a sample data matches a population".
A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".
Assume the following dataset:
Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total
Married 21 37 58 116
Not Married 59 63 42 164
Total 80 100 100 280
Part 1
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is independence between the marital status and the diagnostic of alcoholic
H1: There is association between the marital status and the diagnostic of alcoholic
The level os significance assumed for this case is
Part 2
The statistic to check the hypothesis is given by:
Part 3
The table given represent the observed values, we just need to calculate the expected values with the following formula
And the calculations are given by:
And the expected values are given by:
Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total
Married 33.143 41.429 41.429 116
Not Married 46.857 58.571 58.571 164
Total 80 100 100 280
And now we can calculate the statistic:
Part 4
Now we can calculate the degrees of freedom for the statistic given by:
And we can calculate the p value given by:
And we can find the p value using the following excel code:
"=1-CHISQ.DIST(19.72,2,TRUE)"
Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.