Question

Determine if a significant relationship exists between a persons weight and his/her restaurant bill. The correlation coefficient between these two variables is calculated at 0.622 for a sample of 10 people. Perform a hypothesis test at the level of 0.05 using the classical approach.

1. What are the appropriate hypotheses?

2. What parameter is being tested?

3. What is the critical value off the "critical values of r" table?

4. Whats the decision?

Answer 1

a) As we are trying to test here whether there is a significant correlation between the 2 variables, therefore the null and the alternate hypothesis here are given as:

H0: r = 0

Ha :

b) The parameter being tested here is the correlation coefficient.

c) The table for critical values is shown below:

For n = 10 as the sample size and for 0.05 level of significance, we get from the above table the critical value as: 0.576

Therefore 0.576 is the required critical value here.

d) As the correlation coefficient value here is 0.622 > 0.576 which is the critical value, therefore the test is significant and we can reject the null hypothesis here and conclude that there is significant correlation between the 2 variables.