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