Correlation coefficient

• When do we reject H0?

  If the correlation coefficient>C.V, this means it is unlikely that this value occurred by chance, so the null hypothesis is rejected. 
• When do we accept H0?


  If the correlation coefficient<C.V this means it is likely that this value occurred by chance, so the null hypothesis is not rejected. 
• She collects data on 50 seven-year-olds, which gives a correlation coefficient of -0.3608 The critical value for a two-tailed test with n = 50 at the 5% significance level is 0.2787. Carry out a hypothesis test at the 5% level .

    

  H0: p= 0 H1 : p not = 0 where p is the correlation coefficient for the parent population.  

  Since 0.3608 > 0.2787, reject H0. There is evidence to suggest that there is correlation between time spent using computers and reading ability.  
• How do you interpret the results of correlation coefficient hypothesis testing?

  If the **p-value** is less than the significance level ($\alpha$), reject the null hypothesis and conclude there is a significant correlation. Otherwise, fail to reject the null hypothesis.