Final answer:
The student's conclusion is not valid because the calculated correlation coefficient value is not less than the critical value.
Step-by-step explanation:
The student's conclusion is not valid. In order to determine the significance of the correlation coefficient, we need to compare it to the critical value. According to the information provided, the critical value for the correlation coefficient with four degrees of freedom is 0.811. Since the calculated value of 0.81 is not less than the critical value, we do not reject the null hypothesis and cannot conclude that the correlation is statistically significant.