A study examines self esteem and depression in children using a standardized test for depression. For the general population, scores on this test form a normal distribution with a mean of 90 and a standard deviation of 15. The researcher selects a sample of 25 children with low self-esteem, and conducts a hypothesis test (a=.05) to determine whether children with low self esteem are at increased risk and show more depression than the general population.
a) If the true mean score on this depression test for the population of children with low self esteem is 92.25, what is the power of the hypothesis test to detect this effect?
b)What is the probability of committing a type 2 error for this hypothesis test?