If a population is in Hardy-Weinberg Equilibrium, what conditions must have been met? If the population is not in HW Equilibrium, what are possible explanations as to why the population is not in equilibrium?
For a population to be in Hardy-Weinberg Equilibrium, we must assume that we are working with a sufficiently large population, that mating is random, and that there are no evolutionary forces at work. If the population is not in equilibrium, one of our assumptions must be wrong. Generally speaking, the population is likely to have an evolutionary force acting on it if it is not in equilibrium, including the possibility of mutation. genetic drift, gene flow/migration, and/or natural selection. H-W Equilibrium is used to assess if changes in population genetics have occurred.
Given a known distribution, how would you calculate the maximum likelihood estimator of the dependent variable?
Take the log of the distribution, differentiate with respect to the dependent variable, set it equal to zero, and solve. This describes the estimator for which the distribution of data has the highest probability of occurring.
Given a set of sample data--say, hourly wages--drawn from an independent and identically distributed random variable with known variance s and unknown mean x, what kind of statistical test should be run to determine if the hourly wage is on average higher than 30? What are the relevant null and alternative hypotheses? Under that test with that null hypothesis, how would you interpret a p-value of .3?
With a known variance, we can preform a z-test for any given confidence level. The null hypothesis in this case would be x <= 30; with the alternative hypothesis being x > 30 (x is the mean). We will only reject the null hypothesis if given substantial evidence from the sample data. If we run this test, and receive a p-value of .3, we would probably not reject our null hypothesis under any reasonable confidence level.