Question

A simple random sample of 10 paired values (x,y) yields the following statistical calculations:

∑x=84, ∑y=601, ∑(x2)=888, ∑(y2)=45077, ∑(xy)=6110, x¯=8.4, y¯=60.1, sx=4.5, sy=31.55.∑x=84, ∑y=601, ∑(x2)=888, ∑(y2)=45077, ∑(xy)=6110, x¯=8.4, y¯=60.1, sx=4.5, sy=31.55.

With a 5% significance level, we wish to test the claim that there is a linear correlation between the variables x and y.

1. Write the claim and the opposite of the claim in symbolic forms. (Use rho for the population linear correlation coefficient and whichever symbols you need of "<", ">", "=", "not =").
Claim:
Its opposite:

2. State the null and alternative hypotheses for testing such a claim. (Use rho for the population linear correlation coefficient and whichever symbols you need of "<", ">", "=", "not =").
H0H0 :
H1H1 :

3. Find n∑(xy)−(∑x)(∑y)=n∑(xy)−(∑x)(∑y)=

4. Find n∑(x2)−(∑x)2=n∑(x2)−(∑x)2=

5. Find n∑(y2)−(∑y)2=n∑(y2)−(∑y)2=

6. The linear correlation coefficient is r=r=  (Round your answer to 4 decimal places)

7. The positive critical value of the correlation coefficient is     (Round your answer to 3 decimal places)

8. The negative critical value of the correlation coefficient is     (Round your answer to 3 decimal places)

9. The final conclusion is
A. There is not sufficient evidence to support the linear correlation between x and y.
B. There is sufficient evidence to support the linear correlation between x and y.
C. There is not sufficient evidence to support the linear correlation between x and y.
D. There is sufficient evidence to reject the linear correlation between x and y.
E. There is not sufficient evidence to reject the linear correlation between x and y.
F. There is not sufficient evidence to reject the linear correlation between x and y.
G. There is not sufficient evidence to support the linear correlation between x and y.

10. The regression equation is ŷ = + x (Make sure you first enter the intercept and then the slope. Round each one of them to 4 decimal places).

Answer 1