Question

From studies it is known that the more the time spent running on a treadmill the more the

         calories will be burnt. Let ρ (rho) denotes the population linear correlation coefficient between

         time spent running on treadmill and calories burnt in the gym then for H₀: ρ=0 vs H₁: ρ≠0 has

         to be verified to support the previous studies. To verify this relationship a random sample of 27

         individuals from gym is selected. Given α (alpha) = 0.05, the minimum simple linear correlation

         coefficient (r) that will reject H₀ will be

         a. 0.3819

         b. 0.3809

         c. 0.3815

         d. 0.3799

Answer 1

Given Sample size, n = 27

Number of degrees of freedom, = n- 2

= 25

SIgnificance level = 0.05

The critical value for correlation coefficient can be found from the below attached table for = 25 degrees of freedom and = 0.05

The critical value for correlation coefficient (r) from the below table = 0.381

The sample correlation coefficient must be greater than 0.381 for Null Hypothesis to be rejected

Here there are two value that are greater than 0.381

One is Option (a) which is 0.3819 and another one is Option (c) which is 0.3815

But we want the minimum sample correlation coefficient that can reject the Null Hypothesis. Here 0.3815 is less than 0.3819

So the minimum sample correlation coefficient that can reject the Null Hypothesis is 0.3815

So Answer is Option C