Answer:
Step-by-step explanation:
Hello!
Given the variables
X₁: Weight of a diamond (carats)
X₂: Price of a diamond (dollars)
You have to test if there is any correlation between the two variables, the hypotheses are:
H₀: ρ = 0
H₁: ρ ≠ 0
α: 0.05
The resulting correlation coefficient is
r= 0.97
I've used statistics software to calculate the correlation coefficient. To do so manually you have to use the following formula:
[tex]r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2-\frac{(sumX_2)^2}{n} ]}[/tex]
The statistic for the parametric test is
[tex]t= \frac{r\sqrt{n-2} }{\sqrt{(1-r^2)} } = \frac{0.97\sqrt{6-2} }{\sqrt{(1-(0.97^2))} } = 7.98[/tex]
p-value 0.0016
The p-value is less than the level of significance, so the decision is to reject the null hypothesis.
Then at a 5% significance level, you can conclude that there is a linear correlation between the weight in carats of the diamonds and their price in dollars.
The scatterplot in the attachment.
I hope you have a SUPER day!
