STAT 440 - Forecasting
Lecture Review #5 - Correlation Inference

NOTE that a handout covering the formulas discussed in class is available here.

Review questions:

1) What is meant by a sampling distribution? What must be true about the sampling distribution, to be able to use normal-theory statistical inference procedures?

2) What is a confidence interval used for? A hypothesis test?

3) When is a z-statistic used? A t-statistic?

4) What is Fisher’s z-transformation and when is it used?

Computational exercises:

Balph Snerdwell is investigating whether carbonated caffeine makes you smarter. He conducts a small experiment, using fourteen laboratory rats. He gives different rats different amounts of carbonated caffeine, and measures how long it takes (how many trials) for the rat to learn to run a maze. (Well, "walk" a maze, actually. Running is bad for rats.) He computes a sample correlation of –0.42 for his data.

a) What does the negative sign mean on the correlation coefficient?

b) How much of rat intelligence (or, at least, maze-learning skill) is "explained" by carbonated caffeine consumption?

c) Is Balph’s correlation statistically significant? (Has he demonstrated a relationship between the two variables?)

d) Give a 95% confidence interval for the true population correlation coefficient.

e) Using these data, test H₀: ρ = -0.5 vs. H_A: ρ ≠ -0.5 .

SOLUTIONS:
c) t = -1.60, 12 df
d) -.77 to -.14
e) z = .339