The data below shows the selling price (in hundred thousands) and the list price (in hundred thousands) of homes sold. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using $\alpha = 0.05$.
Is there sufficient evidence to conclude that there is a linear correlation between the two variables?
Selling Price (x) 404 301 377 430 456 478 315 355 417 330
List Price (y) 412 316 389 439 488 480 322 368 431 343
Is there sufficient evidence to conclude that there is a linear correlation the two variables?
Select all TRUE statements for the above hypothesis test from those given below.
Answer
1. $H_0: \rho = 0 H_1: \rho \ne 0$
2. The linear correlation coefficient is 0.992.
3. The test statistic is -21.975
4. The P-value = 0.000
5. Because the P-value is less than the significance level 0.05, there is sufficient evidence to support the claim that there is a linear correlation between the selling price (in hundred thousands) and the list price (in hundred thousands) of homes sold for a significance level of $\alpha = 0.05$.