Question

You have tested to find whether a relationship exists between hours of sleep the night before an exam and grade on the exam. You have a participant pool of n=28, df=26. Your hypothesis is that a significant relationship will exist, where those with more hours of sleep receive higher grades on the exam. This is a directional hypothesis, so you run a one-tailed test, with α=0.05. You run the numbers and find a correlation of 0.243. Doing the math, you find t=1.278. The critical value needed is ____________ and you conclude that your correlation is ___________.

a) 1.708, significant
b) 1.708, not significant
c) 1.701, significant
d) 1.701, not significant

Answer 1

The critical value for a one-tailed test with 26 degrees of freedom at α=0.05 is 1.708; since the calculated t-value of 1.278 is less, the correlation is not significant (b) 1.708, not significant.

Step-by-step explanation:

Asking about whether the relationship between hours of sleep and exam grade is statistically significant, based on your findings of a correlation of 0.243 and a t-value of 1.278. Given that the degrees of freedom (df) are 26 for a one-tailed test at an alpha level of 0.05, you would refer to a t-distribution table to find the critical t-value. The t-distribution table indicates that the critical value for a one-tailed test with df=26 at α=0.05 is approximately 1.708. Because your calculated t-value of 1.278 is less than the critical value of 1.708, you fail to reject the null hypothesis. Therefore, the correct answer to your question is b) 1.708, not significant.