What is the vertex of the parabola
1 answer:
Let's consider the equation of parabola, y = a·(x - α)·(x - β)
where α, β are the x-intercepts.
From the given graph, the y-intercept is (0, -3).
From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.
So the equation of parabola would be now, y = a·(x + 1)·(x - 3)
We can plug the y-intercept (0, -3) in the equation to find value of 'a'.
-3 = a·(0+1)·(0-3)
-3 = -3a
a = 1
So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3
Comparing it with y = ax² + bx + c
The x-coordinate of vertex would be,
the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.
Hence, vertex would be (1, -4).
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Answer:
Because the P-value is _(<u>0.02) less </u> than the significance level 0.05, there <u> is </u> sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α=0.05.
C. The results suggest that imported lemons cause car fatalities.
Step-by-step explanation:
Hello!
The study variables are:
X₁: Weight of imported lemons.
X₂: Car crash fatality rate.
The objective is to test if the imported lemons affect the occurrence of car fatalities. To do so you are asked to use a linear correlation test.
I've made a Scatterplot with the given data, it is attached to the answer.
To be able to use the parametric linear correlation you can use the parametric test (Person) or the nonparametric test Spearman. For Person, you need your variables to have a bivariate normal distribution. Since one of the variables is a discrete variable (ratio of car crashes) and the sample is way too small to make an approximation to a normal distribution, the best test to use is Spearman's rank correlation.
This correlation coefficient (rs) takes values from -1 to 1
If rs = -1 this means that there is a negative correlation between the variables
If rs= 1 this means there is a positive correlation between the variables
If rs =0 then there is no correlation between the variables.
The hypothesis is:
H₀: There is no linear association between X₁ and X₂
H₁: There is a linear association between X₁ and X₂
α: 0.05
To calculate the Spearman's correlation coefficient you have to assign ranks to the observed values of each variable, from the smallest to the highest). Then you have to calculate the difference (d)between the ranks and the square of that difference (d²). (see attachment)
The formula for the correlation coefficient is:
rs= -1
For this value of the correlation coefficient, the p-value is 0.02
Since the p-value (0.02) is less than the significance level (0.05) the decision is to reject the null hypothesis. In other words, there is a linear correlation between the imported lemons and the car crash fatality ration, this means that the modification in the lemon import will affect the car crash fatality ratio.
Note: the correlation coefficient is negative, so you could say that there is a correlation between the variables and this is negative (meaning that when the lemon import increases, the car crash fatality ratio decreases)
I hope it helps!
