Question 648031: Answer the following questions in one or two well-constructed sentences.
a. What happens to the standard error of a sampling distribution as the size of the sample increases?
b. What happens to the distribution of the sample means if the sample size in increased?
c. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! as the size of the sample increases, the standard error decreases.
standard error equals standard deviation of population divided by square root of sample size.
bigger sample size means bigger denominator resulting in smaller standard error.
if the sample size increases, the distribution of sample means becomes more normal.
this is the main idea of the central limit theorem. even if the population distribution is not normal, the distribution of sample means becomes more normal the larger the sample size.
the benefit of larger sample sizes is that the mean of the sample will be closer to the actual population mean and the standard error will be less. the sample mean will be closer to the population mean because the sample size is larger. this also results in a smaller standard error. this also results in a more normal distribution which increases the accuracy of using the z-tables when determing deviations from the population mean.
note that the z-tables assume a normal distribution.
note that, even if the underlying population is not normal, the distribution of sample means becomes more normal as the sample size increases.
bigger sample size results in more accurate results. the sample mean is closer and the deviations from that sample mean are less so your answer is going to have less variance in it making the margin of error less.
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