Young et al. (2006) took measurements of subordinate female meerkats to determine the changes in reproductive physiology experienced by females that are evicted from their social groups. They compared evicted females and those not evicted in their level of plasma luteinizing hormone following a GnRH hormone challenge. They found that 9 evicted females had a sample average of 6.2 mIU/ml (milli-International Units per milliliter) of plasma luteinizing hormone compared with 12.1 mIU/ml in 18 females that had not been evicted. The pooled sample variance was 28.4.

a. Is this an experimental study or an observational study? Explain.

b. The sample size was unequal between the two groups of females compared. How would this affect the power of a hypothesis test of the difference between group means compared with a more balanced design? Explain.

c. How would the imbalance of the sample sizes affect the width of the confidence interval for the difference between group means compared with a more balanced design? Explain.

d. If you were planning to repeat the comparison of plasma luteinizing hormone between these two groups of females, what sample size would you plan to achieve an expected half-width of 3 mIU/ml for a 95% confidence interval of the difference between means? Explain the steps you took to determine this value.