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Answer:
For samples of size n=200, the standard error is of 0.033.
For samples of size n=300, the standard error is of 0.027.
For samples of size n=400, the standard error is of 0.024.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
The percentage of married couples who own a single family home is 33% for a given population.
This means that
Samples of 200:
For samples of size n=200, the standard error is of 0.033.
Samples of 300:
For samples of size n=300, the standard error is of 0.027.
Samples of 400:
For samples of size n=400, the standard error is of 0.024.