25. You are using multilevel regression and poststratification (MRP) to a survey of 1500 people to estimate support for the space program, by state. The model is fit using, as a state- level predictor, the Republican presidential vote in the state, which turns out to have a low correlation with support for the space program. Which of the following statements are basically true? (Indicate all that apply.)

(a) For small states, the MRP estimates will be determined almost entirely by the demo- graphic characteristics of the respondents in the sample from that state.

(b) For small states, the MRP estimates will be determined almost entirely by the demographic characteristics of the population in that state.

(c) Adding a predictor specifically for this model (for example, a measure of per-capita space-program spending in the state) could dramatically improve the estimates of state-level opinion.

(d) It would not be appropriate to add a predictor such as per-capita space-program spending in the state: by adding such a predictor to the model, you would essentially be assuming what you are trying to prove.

Solution to question 24

From yesterday:

24. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. The following sampling designs are considered:

(a) Sample 10 stores, then sample half the vegetables within each of these stores; or

(b) Sample 20 stores, then sample one-quarter of the vegetables within each of these stores.

Which of these designs has the lowest variance? Why might the higher-variance design still be chosen?

Solution: Design (b) has lower variance but design (a) is cheaper.