The distribution of family size in a particular tribal socie

The distribution of family size in a particular tribal society is skewed to the right, with a mean of 5.2 and a standard deviation of 3.0. These values are not known to an anthropologist who samples families in their society to estimate mean family size. For a random sample of 36 families, she gets a mean of 4.6 and a standard deviation of 3.2.

Identify the population distribution, and give numerical values of the mean and standard deviation.

Identify the sample distribution, and give numerical values of the mean and standard deviation.

Identify the sampling distribution of the sample mean, and give numerical values of the mean and standard deviation.

Solution

1. Lognormal distribution, mean = 5.2, and standard deviation = 3.0

2. Lognromal distribution, mean = 4.6, and standard deviation = 3.2

3. Normal distribution, mean = 5.2 and standard deviation = 3.0/6