Question

A researcher working for the Ray-Ban Corporation decides to perform a hypothesis test to investigate whether there is a significant positive correlation
between monthly temperature and number of sunglasses sold at one of their locations.  
The researcher randomly selected the following sample from this location.  
Monthly Temperature (°F)                    Number of Sunglasses Sold
                        80                                                   91
                     61                                                   34
                     56                                                   66
                     99                                                   72
                     71                                                   74
                   95                                                  125
                     43                                                    65

The decision rule for this hypothesis test at α= 5% is:

	a.	Reject Ho if the test statistic is greater than the critical r value r α = 0.58.
	b.	Reject Ho if the test statistic is less than the critical r value r α = - 0.58.
	c.	Reject Ho if the test statistic is greater than the critical r value r α =  0.67.
	d.	Reject Ho if the test statistic is either less than the critical r value r α = - 0.75 or greater than the critical r value r α = 0.75
	e.	Reject Ho if the test statistic is less than the critical r value r α =  - 0.67.

Answer 1

Here we have to test Ho : $\rho$ = 0 Vs Ha : $\rho$ > 0

For level of significance a = 0.05 and d.f =n -2 = 5

r critical = r_{​​​​​​a}​​​​​ = 0.67

So the decision rule is

Reject Ho if the test statistic is greater than the critical r value r _α =  0.67