1. According to the U.S. Census Bureau, the number of people in a household

has a mean of 2.6 and a standard deviation of 1.5. Suppose the Census Bureau instead had

estimated this mean using a random sample of 225 homes, and that sample had a mean of

2.4 and standard deviation of 1.4.

For the sampling distribution of y:

1. specify its mean and its standard deviation (standard error).
2. specify its shape.
3. Sketch the sampling distribution of the sample mean for n = 225.
4. Describe the center and spread of the sample data distribution.

2. (True/False) The central limit theorem implies that:

1. All variables have bell-shaped sample data distributions if a random sample contains at least 30 observations.
2. Population distributions are normal whenever the population size is large.
3. For large random samples, the sampling distribution of y is approximately normal, regardless of the shape of the population distribution.
4. The sampling distribution looks more like the population distribution as the sample size increases.