![]() Compare the standard deviation of vmeans to the quantity 1/10 - 0.316. (In statistics parlance, the standard deviation of a statistic's sampling distribution is called the statistic's standard error.) Compare the mean of vmeans to the mean of a standard normal distribution. Compute the mean and standard deviation of vmeans. Then depict the (empirical) sampling distribution for the sample mean (for samples with size 10) by creating a histogram of vmeans with 30 bins. Repeat part (A) a thousand times, storing the vector of means in a variable vmeans. Generate a random sample of size 10 from a standard normal random variable and store its mean in a variable x. The sampling distribution for the sample mean (for samples of size n) is the probability distribution for these sample mean values. These stored means will generally be different because the samples will generally contain different numbers. Then rinse and repeat: take another sample of size n, compute and store the mean then another sample, compute and store the mean. We take a random sample of size n from some population (which in this exercise we'll assume has a known, standard normal distribution) and we compute and then store the mean of the sample. First, let's quickly review some terminology. ![]() This exercise explores sampling distributions of the sample mean for several sample sizes. ![]()
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