A wire of length 240 inches is cut into 2 equals pieces. Each piece of wire is then bent into forming an equilateral triangle an
1 answer:
240 inches cut into 2 equal pieces is just taking half of the wire.
Making the two pieces of wire 120 inches.
If you bend one 120 inch wire into a square, that means that each side equals 30 inches. (A square has 4 sides. 120/4 = 30)
An area of a square is length times width, which the length equals 30 and width equal to thirty. 30 * 30 = 900. square inches.
120 wire bent into a triangle makes each side equal to 40. 120/3=40. The area of an equilateral triangle is height times width. The width is just one of the sides (40 inches) but the height needs some geometry. To find the height you need to use either 30 times sin(60) or 30 times cos(30), both are equal. To be clear, I will leave the height as 30sin(60). The area will be equal to
which can be simply written as 1200sin(60).
So the sum of both areas is
Making the two pieces of wire 120 inches.
If you bend one 120 inch wire into a square, that means that each side equals 30 inches. (A square has 4 sides. 120/4 = 30)
An area of a square is length times width, which the length equals 30 and width equal to thirty. 30 * 30 = 900. square inches.
120 wire bent into a triangle makes each side equal to 40. 120/3=40. The area of an equilateral triangle is height times width. The width is just one of the sides (40 inches) but the height needs some geometry. To find the height you need to use either 30 times sin(60) or 30 times cos(30), both are equal. To be clear, I will leave the height as 30sin(60). The area will be equal to
which can be simply written as 1200sin(60).
So the sum of both areas is
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Answer:
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(19.221,2,TRUE)"
Since the p values is higher than a significance level for example , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.
Step-by-step explanation:
Previous concepts
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".
Solution to the problem
Assume the following dataset:
Size Company/ Heal. Ins. Yes No Total
Small 32 18 50
Medium 68 7 75
Large 89 11 100
_____________________________________
Total 189 36 225
We need to conduct a chi square test in order to check the following hypothesis:
H0: independence between heath insurance coverage and size of the company
H1: NO independence between heath insurance coverage and size of the company
The statistic to check the hypothesis is given by:
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:
Size Company/ Heal. Ins. Yes No Total
Small 42 8 50
Medium 63 12 75
Large 84 16 100
_____________________________________
Total 189 36 225
And now we can calculate the statistic:
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(19.221,2,TRUE)"
Since the p values is higher than a significance level for example , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.