Young et. al. (2006) took measurements of subordinate female meerkats to determine the changes in reproductive physiology experienced by females that are evicted from thier social group. They compared evicted females and those not evicted in thier level of plasma luteinizing hormone following a GnRH hormone challenge. They found that nine evicted females had a sample average of 6.2 mlU/ml (milli-International Units per milliliter) of plasma luteinizing hormone compared with 12.1 mlU/ml in 18 females that had not been evicted. The pooled sample varience was 28.4 a. Is this an experiemtnal study or an observational study? Explain. b. the sample size was unequal between teh two groups of females compared. How woudl 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 imbalnce 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 luteinzing hormone between these two groups of females, what sample size would you plan to achieve an expercted half width of 3mlU/ml of a 95% confidence interval of the difference between means?