Answer:
r = 0.9825; good correlation.
Step-by-step explanation:
One formula for the correlation coefficient is
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7Bn%5Cleft%20%5B%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5B%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D)
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
<u> </u><u>x</u> <u> y </u> <u> xy </u> <u> x² </u> <u> y² </u>
-3 -40 120 9 1600
1 12 12 1 144
5 72 360 25 5184
<u> 7</u> <u>137</u> <u> 959</u> <u>49</u> <u>18769
</u>
Σ = 10 181 1451 84 25697
2. Calculate the correlation coefficient
![r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{4\times 1451 - 10\times 181}{\sqrt{[4\times 84 - 10^{2}][4\times25697 - 181^{2}]}}\\\\= \dfrac{5804 - 1810}{\sqrt{[336 - 100][102788 - 32761]}}\\\\= \dfrac{3994}{\sqrt{236\times70027}}\\\\= \dfrac{3994}{\sqrt{16526372}}\\\\= \dfrac{3994}{4065}\\\\= \mathbf{0.9825}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bn%5Csum%7Bxy%7D%20-%20%5Csum%7Bx%7D%20%5Csum%7By%7D%7D%7B%5Csqrt%7B%5Cleft%20%5Bn%5Csum%7Bx%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7Bx%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%5Cleft%20%5Bn%5Csum%7By%7D%5E%7B2%7D-%5Cleft%20%28%5Csum%7By%7D%5Cright%20%29%5E%7B2%7D%5Cright%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B4%5Ctimes%201451%20-%2010%5Ctimes%20181%7D%7B%5Csqrt%7B%5B4%5Ctimes%2084%20-%2010%5E%7B2%7D%5D%5B4%5Ctimes25697%20-%20181%5E%7B2%7D%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B5804%20-%201810%7D%7B%5Csqrt%7B%5B336%20-%20100%5D%5B102788%20-%2032761%5D%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B236%5Ctimes70027%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B%5Csqrt%7B16526372%7D%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B3994%7D%7B4065%7D%5C%5C%5C%5C%3D%20%5Cmathbf%7B0.9825%7D)
The closer the value of r is to +1 or -1, the better the correlation is. The values of x and y are highly correlated.
Answer:
The approximate probability that more than 360 of these people will be against increasing taxes is P(Z> <u>0.6-0.45)</u>
√0.45*0.55/600
The right answer is B.
Step-by-step explanation:
According to the given data we have the following:
sample size, h=600
probability against increase tax p=0.45
The probability that in a sample of 600 people, more that 360 people will be against increasing taxes.
We find that P(P>360/600)=P(P>0.6)
The sample proposition of p is approximately normally distributed mith mean p=0.45
standard deviation σ=√P(1-P)/n=√0.45(1-0.45)/600
If x≅N(u,σ∧∧-2), then z=(x-u)/σ≅N(0,1)
Now, P(P>0.6)=P(<u>P-P</u> > <u>0.6-0.45)</u>
σ √0.45*0.55/600
=P(Z> <u>0.6-0.45)</u>
√0.45*0.55/600
Answer:
Conclusion
There is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean
Step-by-step explanation:
From the question we are told that
The population mean for EBR is 
The sample mean for Ascension parish is 
The p-value is 
The level of significance is 
The null hypothesis is 
The alternative hypothesis is 
Here
is the population mean for Ascension parish
From the data given values we see that

So we fail to reject the null hypothesis
So we conclude that there is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean
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