Question

You want to study incomes in a large city. You take a simple random sample of 5012 households and find that the distribution of household incomes is skewed right. If you calculate the mean of the 5012 household incomes will the distribution of mean scores be skewed right as well? Hint: this involves the Central Limit Theorem.

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Answer to a math question You want to study incomes in a large city. You take a simple random sample of 5012 households and find that the distribution of household incomes is skewed right. If you calculate the mean of the 5012 household incomes will the distribution of mean scores be skewed right as well? Hint: this involves the Central Limit Theorem.

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Hank

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To determine whether the distribution of mean scores will be skewed right, we need to consider the Central Limit Theorem. According to the Central Limit Theorem, if we have a large enough sample size, the distribution of sample means will approximate a normal distribution, regardless of the shape of the original population distribution.

In this case, we have a simple random sample of 5012 households, which is considered to be a large sample size. Therefore, we can assume that the distribution of mean incomes will be approximately normal.

Answer: No, the distribution of mean scores will not be skewed right. It will resemble a normal distribution due to the Central Limit Theorem.

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