You wish to determine if there is a negative linear correlation between the two variables at a significancelevel of a = 0.005. You have the following bivariate data set.25.48.11638.114.537.929.730.22.7Hn: Select an answer V= 0H: Select an answerOriginal claim =OH:O HoNote: In your calculations, except for the p-value and the graph, round both r and t to 3 decimal places inALL calculations. What is the correlation coefficient for this data set?To find the p-value for a correlation coefficient, you need to convert to a t-score:r2(n – 2)t =1- 12This t-score is from a t-distribution with n-2 degrees of freedom.t= What is the p-value for this correlation coefficient?p-value =(Round to four decimal places.)Critical Value = t(0.005,3)=Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. Thearrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these valuescorrespond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left,to the right, between or left and right of the t-score(s).Shade: Left of a valuev. Click and drag the arrows to adjust the values.++-4-3-2 1 -1234-1.5Decision: Select an answerConclusion: Select an answerthe claim that there is a negative linearcorrelation between the two variables.

Answered: You wish to determine if there is a…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 23PFA

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Question

You wish to determine if there is a negative linear correlation between the two variables at a significance
level of a = 0.005. You have the following bivariate data set.
25.4
8.1
16
38.1
14.5
37.9
29.7
30.2
2.7
Hn: Select an answer V
= 0
H: Select an answer
Original claim =
OH:
O Ho
Note: In your calculations, except for the p-value and the graph, round both r and t to 3 decimal places in
ALL calculations. What is the correlation coefficient for this data set?
To find the p-value for a correlation coefficient, you need to convert to a t-score:
r2(n – 2)
t =
1- 12
This t-score is from a t-distribution with n-2 degrees of freedom.
t=

What is the p-value for this correlation coefficient?
p-value =
(Round to four decimal places.)
Critical Value = t(0.005,3)=
Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The
arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values
correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left,
to the right, between or left and right of the t-score(s).
Shade: Left of a value
v. Click and drag the arrows to adjust the values.
++
-4
-3
-2 1 -1
2
3
4
-1.5
Decision: Select an answer
Conclusion: Select an answer
the claim that there is a negative linear
correlation between the two variables.

Expert Solution

Step 1 : Hypotheses.

Claim : There is a negative linear correlation between the two variables.

Based on the above claim the null and alternative being tested is ,

Null hypotheses , Ho : ρ = 0.

Alternative hypotheses , H₁ : ρ < 0.

The directional of this is left tailed test .

Note : left and right tailed tests both comes under one tailed test.

Original claim : H₁.

Step 2 : Correlation , r.

It is asked to calculate correlation coefficient , r for the given data set.

It can be easily calculated by using MS_EXCEL.

Please refer the following steps.

Enter your x and y data in excel.
Use =CORREL ( array 1 , array2 ) function to calculate r.

it will look like ,

Statistics homework question answer, step 2, image 1

Now hit on enter to get the correlation coefficient (r) and it is equal to -0.79684 till 3 decimal places it would be -0.797.

Thus , the correlation coefficient (r) for this data set is -0.797.

Step 3 : t score.

The formula to calculate t score is ,

$\begin{array}{rcl} t & = & \sqrt{\frac{r ² (n - 2)}{1 - r ²}} \\ = & \sqrt{\frac{(- 0.797) ² (5 - 2)}{1 - (- 0.797) ²}} \\ = & 2.286 \end{array}$

Note : n is the numbers in your data set (either in x or y) so it is equal to 5.

Thus , t score = 2.286.

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