SOLUTION: A small town has 2500 families. the average number of children per family is 3.2, with a standard deviation of 0.5; the distribution is skewed. A researcher wants to draw a random

Question 1072430: A small town has 2500 families. the average number of children per family is 3.2, with a standard deviation of 0.5; the distribution is skewed. A researcher wants to draw a random sample of 100 families from the small town and record the number of children in each family. Her statistical inference would be based on a sampling distribution pf all possible samples of size 100.
(a) What is the mean of the sampling data?
(b) What is the standard deviation of the sampling distribution of all possible sample means?
(c) What is the shape of the sampling distribution of all possible sample means? Explain why
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The sample size is 100 / 2500 = 1/25 of the population which is a significant proportion of the population.
:
a) the mean of the sample is the same as the population mean which is 3.2
:
b) the standard deviation of the sampling distribution(SE) is calculated with the following formula
:
standard error(SE) = (0.5 / square root(100)) * square root( (2500 - 100) / (2500 - 1))
:
SE = 0.0495
:
c) since the population distribution is skewed, we need sample size > 40 to ensure that the sample distribution approximates a normal distribution
:

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