[p_goral]

:o

True False According to the central limit theorem, the standard deviation of the distribution of sample means will be the original population standard deviation divided by N (the sample size).
True False According to the central limit theorem, the mean of the distribution of sample means will be the same as the original population mean.
True False The typical distance of a sample mean from the true population mean is measured by the standard error of the means.
True False If the original population has a positively skewed distribution, the distribution of sample means for that population, with N = 100 for each sample, will have a positively skewed distribution.
True False The central limit theorem always holds true, regardless of the sample size.

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A researcher interested in the effectiveness of a smoking cessation program does a study in which she measures the number of cigarettes smoked by each person entering the program. Since the number of cigarettes smoked is a "counting variable", the population distribution is positively skewed. That is, most people smoke somewhere around 20 or 30 cigarettes a day, but a few people smoke 100 cigarettes or more each day. The population mean number of cigarettes smoked is 20.1 and the population standard deviation is 5.93.
What does the Central Limit Theorem tell us about the distribution of sample means from this population when the sample size is 96?

True False The standard deviation of the distribution of sample means will equal 0.605.
True False The typical distance between the sample means and the population mean is 5.93.
True False The mean of the distribution of sample means will be 20.1.
True False The distribution of sample means will approximate a normal distribution.

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The size of the standard error of the means is partially determined by...

True False the size of the population mean, because populations with lower means give samples with less variable means.
True False the variability of the original population because populations that are more variable give samples that have less similar (more variable) means.
True False sample size because larger samples give sample means that are closer to the true population mean
True False the difference between the mean and the standard deviation of the population because populations with bigger differences between the mean and standard deviation give samples with more variable means.

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:confused: Consider a large population of scores from a positively skewed distribution with mean m = 91 and standard deviation s = 7. Take all possible random samples with 34 in each sample.

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A. According to the Central Limit Theorem, what would the mean of the distribution of sample means be?


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B. What would the standard deviation of the distribution of sample means be?:eek:

[Capuchin]

Hi Ms. goral, I have merged all of your questions because what I am about to say applies to them all:

We will not do your homework for you. You need to show how far you have gotten with the questions before we will help you.

[artissa]

True