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.  

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 (TEMP SUMS: x = 505; E x2 = 38,973) (NBR SUMS: 2 x = 527; E x2 = 44,303) The decision rule for this hypothesis test at a= 5% is: Reject Ho if the test statistic is greater than the critical r value ra 0.67. a. b. a Reject Ho if the test statistic is less than the critical r value r - 0.58. =- C. Reject Ho if the test statistic is greater than the critical r value ra = 0.58. d. Reject Ho if the test statistic is less than the critical r value ra = - 0.67. e. Reject Ho if the test statistic is either less than the critical r value r a = -0.75 or greater than the critical r value ra =0.75

Answer 1

We have Ho : $\rho$ = 0 Vs H1 : $\rho$ > 0

r critical for a= 0.05 and df = n -2 = 5

r_{​​​​​​a}​​​​​ = 0.67

So the decision rule is

Reject Ho if the test statistic is greater than the critical r value r_{​​​​​​a}​​​​​ = 0.67