Mathematics, 21.02.2020 02:31 evazquez

(a) For the accompanying data set, draw a scatter diagram of the data.
x 2 6 6 7 9
y 3 2 6 9 5

(b) by hand compute the correlation coefficient. r = (round to three decimals as needed.)
(c) Fill in the blanks: Because the correlation coefficient is (positive or negative) and the absolute value of the correlation coefficient, , is (greater or not greater) than the critical value for this data set,___, (no, a positive, or a negative) linear relation exists between x and y.

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Answer from: queenz58

a) n=5 $\sum x = 30, \sum y = 25, \sum xy = 162, \sum x^2 =206, \sum y^2 =155$

$r=\frac{5(162)-(30)(25)}{\sqrt{[5(206) -(30)^2][5(155) -(25)^2]}}=0.42967$

So then the correlation coefficient would be r =0.430 rounded

b) Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

Because the correlation coeffcient is positive and the absolute value of the correlation coefficient 0.430 is not greater than the critical value for this dataset, no linear relation exists between x and y.

And the reason is because we fail to reject the null hypothesis.

Step-by-step explanation:

Part a

We have the following data:

x: 2 6 6 7 9

y: 3 2 6 9 5

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=5 $\sum x = 30, \sum y = 25, \sum xy = 162, \sum x^2 =206, \sum y^2 =155$

$r=\frac{5(162)-(30)(25)}{\sqrt{[5(206) -(30)^2][5(155) -(25)^2]}}=0.42967$

So then the correlation coefficient would be r =0.430 rounded

Part b

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degreed of freedom. df=n-2=5-2=3

In our case the value for the statistic would be:

$t=\frac{0.430\sqrt{5-2}}{\sqrt{1-(0.430)^2}}=0.825$

The critical value for n =5 is given by the table attached. We can see that the critical value is $r_{crit}= 0.878$ , and then the final conclusion would be:

And the reason is because we fail to reject the null hypothesis.

(a) For the accompanying data set, draw a scatter diagram of the data. x 2 6 6 7 9 y 3 2 6 9 5 (b) b

Answer from: Quest

i got 86 for this

hope this !

if you need an explanation just ask

Answer from: Quest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

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(a) For the accompanying data set, draw a scatter diagram of the data.
x 2 6 6 7 9
y 3 2...

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