Question

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Test the significance of the correlation coefficient using = 0.05 and the claim = 0. Hours, x Scores, y 4 67 6 82 3 62 9 90 3 68 5 80 5 87 6 92 7 92 4 73

Answer 1

The correlation coefficient values is obtained in excel using the function =CORREL(). The screenshot is shown below,

Now, the hypothesis test for significance of the correlation coefficient is performed in following steps,

Step 1: The null and alternative hypotheses are,

Step 2: The t-statistic is obtained using the formula,

Step 3: The significance level,

The P-value for the t-statistic for degree of freedom = n-2=8 is obtained from t distribution table,

Step 4:

Since the P-value is less than 0.05 at 5% significance level value, the null hypothesis is rejected. Hence there is a significant correlation.