Suppose I want to know whether there is a relationship between how important college students think their statistics work is and the grade they get in their statistics class. I select a random sample of 10 college students and find that the correlation between their ratings of importance and their grade in the statistics course is .40. Using an alpha level of .05, tell me whether that correlation coefficient is statistically significant (i.e., meaningful). Be sure to wrap words around your final result.

Question

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The Answer is r = .40 df = 10-2 = 8

\alpha

= .05 2-tailed
t_c = 2.306
t_o = .4 (8/1-.16)

\rightarrow

.4 (8/.84)

\rightarrow

.4 (9.52)

\rightarrow

.4(3.09)
t_o = 1.23
Because my observed t is smaller than my critical t, I retain the null hypothesis and conclude that, in the population, there is not a significant relationship between how important students think the work is in statistics and the grade they get in their statistics class.

Suppose I Want to Know Whether There Is a Relationship