Homework #1: Stat 422

2.1 An experimenter wants to estimate the average water consumption per family in a city. Discuss the relative merits of choosing individual families, dwelling units (single-family houses, apartment buildings, and so on), as sampling units. What would you use as a frame in each case?

Suppose Home-dwelling families use an additional 20 gallons per individual to water the lawn. So apartment dwelling families water use is distributed N(mean=20,sd=5) and home-dwelling families water use is distributed as N(mean=40,sd=5). If we were in Podunkville, perhaps the population would consist of 10 families from both apartments and homes and could be expressed in the following dot chart:

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## Attaching package: 'combinat'
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## The following object(s) are masked from 'package:utils':
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###The Pure Sample
Now supposing I used a sampling frame of the local telephone book and supposing all 10 families were listed I could see the following.

• There are 120 ways to sample 3 from our 10 families.
  
• The sample means and standard deviations should be compared to the population mean (27.6197)and standard deviation (12.2477).
  

2.4 An industry is composed of many small plants located throughout the United States. An executive wants to survey the opinions of the employees on the vacation policy of the industry. What do you suggest she use as sampling units? As a frame?

3.4 What is a sampling distribution?

3.5 How do we evaluate the goodness of an estimator?

mvrnorm(n1, mu = mu1, Sigma)

## Error: object 'mu1' not found

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