A study involving hypothesis testing is conducted in a major hospital to under- stand the proportion of mothers who stay for less than two days in the hospital after delivery. A sample of 50 births is taken to test whether more than half of all mothers have a length of stay (LOS) of less than two days. Use α = 0.10. If the true proportion of mothers who have a LOS of two days is 0.60, what is the power of the test? What sample size is needed to attain 80% power?