Which of the following are true? Correct false statements to make them true. A)

Question

Which of the following are true? Correct false statements to make them true.

A) The standard error of the distribution of sample means indicates how tightly the sample means are clustered around the population mean.

B) The standard deviation of the distribution of sample means (aka the standard error of the mean, SEM) for all possible samples of size 16 is greater than the standard deviation of the parent population.

C) The standard error is a measure of the uncertainity about the estimate for a population mean that is based on a sample mean

D) Holding other factors constant, the standard deviation of x(bar) (SEM) of samples of size 30 is greater than the standard deviation of x(bar) (SEM) for samples of size 20.

Explanation / Answer

A) The standard error of the distribution of sample means indicates how tightly the sample means are clustered around the population mean - TRUE

B) The standard deviation of the distribution of sample means (aka the standard error of the mean, SEM) for all possible samples of size 16 is greater than the standard deviation of the parent population - False

The standard error will be less than the standard deviation of the parent population

C) The standard error is a measure of the uncertainity about the estimate for a population mean that is based on a sample mean - True

D) Holding other factors constant, the standard deviation of x(bar) (SEM) of samples of size 30 is greater than the standard deviation of x(bar) (SEM) for samples of size 20 - False

Standard deviation of x(bar) decreases with increase in sample size. So, holding other factors constant, the standard deviation of x(bar) (SEM) of samples of size 30 is lesser than the standard deviation of x(bar) (SEM) for samples of size 20.

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