CORRELATION COEFFICIENT TEST

Random sample of 27 pairs of observations obtained from a normal population gives correlation coefficient 0.42.  Test if sample correlation coefficient is similar to population correlation coefficient or variables of population are uncorrelated. Significance level at 5% (t0.05) for 25 d,f =2.06  

Solution

  • Sample size n = 27
  • Correlation Coefficient(sample) r = 0.42
  • Null Hypothesis H0i = 0 Variables are uncorrelated in population
  • Alternative Hypothesis: Variables are correlated

Conclusion: The calculated value (t = 2.312) is greater than tabulated value (t = 2.06) and it falls in the rejection region. So, we reject the Null Hypothesis. The variables in population are correlated  in population