Deck 12: Correlation

Question 1

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.

Answer 1

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.

Question 2

Suppose the standard error of that correlation coefficient in Question 1 is .10. Wrap words around this standard error. What does it tell you, exactly?

Answer 2

The average difference between the population correlation coefficient and the sample correlation coefficients, when the samples are randomly selected and n = 10, is .10.

Question 3

Suppose that I have a randomly selected sample of 42 American men. In this sample, the average number of hours worked per week is 45 with a standard deviation of 12. The average level of life satisfaction (on a scale from 1 = "hating life" to 10 = "loving life) is 5.00 with a standard deviation of 3.00. The correlation between hours worked and life satisfaction is .40. Please answer the following 10 questions based on these data.
a. What does this correlation coefficient tell you about the relationship between hours worked and life satisfaction? (Be thorough-tell me about the strength, direction, and for whom this information applies).
b. If we use an alpha level of .01, is this a statistically significant correlation? Calculate the statistics and wrap words around your results. (Be thorough-tell me all that you know).
c. Please give me one plausible (i.e., reasonable) EXPLANATION for why hours worked and life satisfaction are related to each other this way in this sample.

Answer 3

a. It tells me that in THIS SAMPLE, the relationship between hours worked and life satisfaction is positive and moderate. On average, as the number of hours increases, so does life satisfaction.
b. t = .40 $\surd$ (40/.84) $\rightarrow$ .40* $\surd$ 47.62 $\rightarrow$ .40 * 6.90 = 2.76. The critical t value (2 tailed, .01, 40 df) is 2.704. Because the observed value exceeds the critical value (just barely), I conclude that, on average, hours worked is positively related to life satisfaction in the population.
c. Maybe working more hours is related to making more money, and making more money is related to driving a better car. Everybody likes life better when they drive a better car, no?