Can you tell if a mouse is in pain by looking at its facial expression? A new study believes you can. The study created a ‘‘mouse grimace scale” and tested to see if there was a positive correlation between scores on that scale and the degree and duration of pain (based on injections of a weak and mildly painful solution). The study’s authors believe that if the scale applies to other mammals as well, it could help veterinarians test how well painkillers and other medications work in animals.

(a) Define the relevant parameter(s) and state the null and alternative hypotheses.

(b) Since the study authors report that you can tell if a mouse is in pain by looking at its facial expression, do you think the data were found to be statistically significant? Explain.

(c) If another study were conducted testing the correlation between scores on the ‘‘mouse grimace scale” and a placebo (non-painful) solution, should we expect to see a sample correlation as extreme as that found in the original study? Explain. (For simplicity, assume we use a placebo that has no effect on the facial expressions of mice. Of course, in real life, you can never automatically assume that a placebo has no effect!).

(d) How would your answer to part (c) change if the original study results showed no evidence of a relationship between mouse grimaces and pain?