Final answer:
To calculate the t-value, use the formula: t = (√−2)/√(1−²) with = 0.45 and = 25. Compare the t-value to the critical value to determine if the result is significant. Calculate the p-value using the tcdf function on a calculator.
Step-by-step explanation:
To calculate the t-value, we can use the formula: t = (√−2)/√(1−²), where is the correlation coefficient and is the sample size. In this case, = 0.45 and = 25. Plugging these values into the formula, we get: t = (0.45√25)/√(1−0.45²) = 2.417.
Next, we need to compare the calculated t-value to the critical value to determine if the result is significant. The critical value for a two-tailed test using the t-distribution with 24 degrees of freedom and α = 0.05 is 2.064. Since the calculated t-value (2.417) is greater than the critical value (2.064), we reject the null hypothesis and conclude that the variables are significantly correlated.
Finally, we can calculate the p-value using the tcdf function on a calculator. The p-value for our t-value of 2.417, with degrees of freedom greater than 10^99, is 0.0118. This further supports our conclusion that the variables are significantly correlated.