13. A study seeks to compare hospitals based on the performance of their intensive care units. The dependent variable is the mortality ratio, the ratio of the number of deaths over the predicted number of deaths based on the condition of the patients. The comparison will be between hospitals with nurse staf ng problems and hospitals without such problems.

Assume, based on past experience, that the standard deviation of the mortality ratio will be around .2 in both types of hospital. How many of each type of hospital should be included in the study in order to have both the type I and type II error probabilities be .05, if the true difference of mean mortality ratio for the two types of hospital is .2? If we conclude that hospitals with nurse staf ng problems have a higher mortality ratio, does this imply a causal relationship? Explain.