Can you find the simplest form of this math problem.
2 answers:
You might be interested in
The answer is 2416.5 and i did it on paper
Answer:
1)
2)
And we got the same decision reject the null hypothesis at 5% of significance.
Step-by-step explanation:
Previous concepts
The Chi-Square test of independence is used "to determine if there is a significant relationship between two nominal (categorical) variables". And is defined with the following statistic:
Where O rpresent the observed values and E the expected values.
State the null and alternative hypothesis
Null hypothesis: The distribution is 30% catfish, 15% bass, 40% bluegill, and 15% pike
Alternative hypothesis: The distribution is NOT 30% catfish, 15% bass, 40% bluegill, and 15% pike
The observed values are given by the table given:
Catfish =112, BAss = 95, Bluegill=210, Pike=83
Calculate the expected values
In order to calculate the expected values we can use the following formula for each cell of the table
Part 1: Calculate the statistic
Calculate the critical value
First we need to calculate the degrees of freedom given by:
Since the confidence provided is 95% the significance would be and we can find the critical value with the following excel code: "=CHISQ.INV(0.95,3)", and our critical value would be
We can calculate also the p value:
And we got the same decision reject the null hypothesis at 5% of significance.
Short Answers:
Answer for part A: Given
Answer for part B: Angle A = Angle D (not sure why this isn't in word bank?)
Answer for part C: ASA
Answer for part D: BC = EF
Answer for part E: CPCTC
-------------------------------------------------------------
Explanations:
Part A:
AB = DE is given at the very top of the problem. So we simply say "given". We always repeat what we are given at the very start of the proof. You can see this for lines 1 through 3, which are repeating the three givens.
---------------------
Part B:
The three givens are:
AB = DE
angle A = angle D
angle B = angle E
the first and last of this trio is used (for statements 1 and 3 respectively). So the only thing left is "angle A = angle D"
---------------------
Part C:
We're using ASA (angle side angle) because we're given two pairs of congruent angles. The side for each triangle is between the two angles. See the attached diagram for more info.
---------------------
Part D:
For any proof, you will ALWAYS have the last statement be the thing you want to prove. In this case, we want to prove BC = EF.
---------------------
Part E:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
If the two whole triangles are congruent, then the smaller corresponding parts that make up the triangles must be congruent as well.
Answer for part A: Given
Answer for part B: Angle A = Angle D (not sure why this isn't in word bank?)
Answer for part C: ASA
Answer for part D: BC = EF
Answer for part E: CPCTC
-------------------------------------------------------------
Explanations:
Part A:
AB = DE is given at the very top of the problem. So we simply say "given". We always repeat what we are given at the very start of the proof. You can see this for lines 1 through 3, which are repeating the three givens.
---------------------
Part B:
The three givens are:
AB = DE
angle A = angle D
angle B = angle E
the first and last of this trio is used (for statements 1 and 3 respectively). So the only thing left is "angle A = angle D"
---------------------
Part C:
We're using ASA (angle side angle) because we're given two pairs of congruent angles. The side for each triangle is between the two angles. See the attached diagram for more info.
---------------------
Part D:
For any proof, you will ALWAYS have the last statement be the thing you want to prove. In this case, we want to prove BC = EF.
---------------------
Part E:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
If the two whole triangles are congruent, then the smaller corresponding parts that make up the triangles must be congruent as well.