Question

listed below are annual data for various years. the data are the numbers of cars sold (thousands) and the numbers of points scored in the super bowl. construct a scatterplot, find the value of the linear correlation coefficient r, and find the p - value using α = 0.05. is there sufficient evidence to conclude that there is a linear correlation between those two variables? would it be reasonable to expect a correlation?

car sales	8179	8218	8518	8992	8636	8535	8275	8142

...

what are the null and alternative hypotheses?

○ a. $h_0: \
ho \
eq 0$ $h_1: \
ho = 0$
○ b. $h_0: \
ho = 0$ $h_1: \
ho < 0$
○ c. $h_0: \
ho = 0$ $h_1: \
ho \
eq 0$
○ d. $h_0: \
ho = 0$ $h_1: \
ho > 0$

Explanation:

To test for a linear correlation between two variables, the null hypothesis (\(H_0\)) assumes no linear correlation (i.e., the population correlation coefficient \(
ho = 0\)). The alternative hypothesis (\(H_1\)) for a two - tailed test (since we are just testing if there is a linear correlation, not a specific direction) is that there is a linear correlation (\(
ho
eq0\)). Option A has the null and alternative hypotheses reversed. Options B and D are one - tailed tests (testing for negative or positive correlation respectively), but we don't have a prior reason to assume a direction. So the correct hypotheses are \(H_0:
ho = 0\) and \(H_1:
ho
eq0\) which is option C.

Answer:

C. \(H_0:
ho = 0\)
\(H_1:
ho
eq0\)