STA2023 Homework 3

Central limit theorem can be applied only when samples are from Normal populations.

False

From the central limit theorem, we know that is we draw a SRS from any population then the sampling distribution of the sample mean will be EXACTLY Normal.

False

True or false: The central limit theorem tells us about the sampling distribution of the sample standard deviation.

False

The Central Limit Theorem says that if the sample size is large enough

the distribution of the sample mean gets closer to being shaped like a normal distribution.

Whenever a sampled population is normally distributed or whenever the conditions of the central limit theorem are fulfilled, the sample mean is a(n):

unbiased estimator of the population mean, mu, because the mean of the sampling distribution of the sample mean equals mu.

Select the correct choice. To apply the CLT, the typical rule of thumb for setting sample size is greater than or equal to what?

30

Select the correct choice. Something with a standard normal distribution has a mean of ____ and a standard deviation of 1.

0

Based on the central limit theorem, the sampling distribution of the sample mean becomes more Normal as the sample size ______.

Increases

Select the correct choice. The sampling distribution is essentially constructed by creating a histogram of individual sample ______.

Means

Asked was the central limit theorem says, a student replies, As you take large and larger samples from a population, the histogram of the sample values look more and more Normal. Is the student right?

No. The central limit theorem says nothing about the histogram of the sample values. It deals only with the distribution of the sample's mean.

Which statement about the Central Limit Theorem is TRUE?

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n>30)