Carmen Homework 11 - Sampling Distributions

Which of the following describes the relationship between parameters and statistics?

We use statistics to estimate or test parameters.

If X does not have a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar?

X-bar is approximately normal if n > 30.

If X has a normal distribution, which of the following is true about the shape (distribution) of the random variable X-bar?

X-bar is exactly normal for any n.

What is the symbol we use to represent the mean of the random variable X-bar?

Mu with subscript X-bar

Which of the following is true about the mean of the random variable X-bar as n increases?

The mean of X-bar stays the same.

The set of all possible sample means from all possible samples of size n from the population is known as the:

Sampling distribution of X-bar

A company has developed a new battery, but the average lifetime of all of the batteries it makes is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a:

Statistic

The Central Limit theorem tells us important results that pertain to:

The shape (type) of the distribution of X-bar.

Which of the following is true about the standard error of the random variable X-bar as n increases?

The standard error of X-bar decreases.

How large does n generally have to be in order for the Central Limit Theorem to take effect? (Assume X does not have a normal distribution.)

n > 30