. Describe the conditions under which a researcher would delete a case with missing data versus the conditions under which a researcher would use an imputation method. Evaluate the following statement: In order to run most mul- tivariate analyses, it is not necessary to meet all the assump- tions of normality, linearity, homoscedasticity, and independence. Discuss the following statement: Multivariate analyses can be run on any data set, as long as the sample size is adequate. 1 Convenience Store A small but busy convenience store has room in its building for only 4 customers. It has 2 employees who work (interchangeably) waiting on customers and performing other tasks (such as stocking shelves). The work rule the employee follow is this: When there are 3 or 4 customers in the store, both wait on customers. When there are 2 or fewer customers in the store, only 1 employee waits on customers. Customers arrive at the store according to a Poisson process with rate A = 1 (and go away if there is no room in the store). We will assume that they spend no time finding their items and that either employee can service them at a rate = 0.8. (a) Carefully draw an appropriate birth and death process transition rate diagram for this scenario. (b) What is the (large t) probability that there is no customer in the store? (c) What is the probability that there are less than 3 customers in the store? (d) What is the probability that an arriving customer is turned away? 6. Consider a stationary stochastic process XX with covariance function R = cov(X, X ) = 3k for k = 0, 1, 2, 3, and R = 0 for k 4. Find Var(X). 1+k Question 13 5 pts What is the difference between internal validity and external validity? A statistical analysis is said to have external validity if the statistical inferences about causal effects are valid for the population being studied. The analysis is said to have internal validity if conclusions can be generalized to other populations and settings. A statistical analysis is said to have internal validity if the statistical inferences about causal effects are valid for the population being studied. The analysis is said to have external validity if conclusions can be generalized to other populations and settings. A statistical analysis is said to have internal validity if the statistical inferences about causal effects can only be verified by a few researchers. The analysis is said to have external validity if conclusions can be verified by many researchers. Internal validity and external validity are equivalent.