To find out whether students scores in physics have significant relationship with their scores in math, the person product moment correlation coefficient of 0.60 for 50 students was gotten. Given the critical value; t(49; 0.05) = 2.021.
1) State the propose null hypothesis
2) Is the propose null hypothesis significant?
To determine the significance of the relationship between students' scores in physics and their scores in math, we need to test the null hypothesis.
1) The null hypothesis (H0) states that there is no significant relationship between students' scores in physics and their scores in math. In other words, the correlation coefficient is equal to zero (ρ = 0).
2) To test the significance of the null hypothesis, we can use the critical value of t for a given level of significance (α). In this case, the critical value is t(49, 0.05) = 2.021, where the degrees of freedom (df) equal 49 (number of students - 1) and the level of significance α is 0.05.
Now, to determine whether the null hypothesis is significant or not, we compare the obtained correlation coefficient value (r) with the critical value (t). In this case, the person product moment correlation coefficient is given as r = 0.60.
If the absolute value of r is greater than the critical value of t, then we reject the null hypothesis and conclude that there is a significant relationship. Conversely, if the absolute value of r is less than or equal to the critical value of t, we fail to reject the null hypothesis and conclude that there is no significant relationship.
In this example, since the obtained correlation coefficient value (r = 0.60) is greater than the critical value of t (2.021), we can conclude that the proposed null hypothesis is not significant. Therefore, there is a significant relationship between students' scores in physics and their scores in math.