week 11 carmen quiz: sampling distributions and confidence intervals for mean

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

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 margin of error is larger if the standard deviation of the population increases (assume all else stays the same.)

true

We are 100% confident that our SAMPLE mean is in every confidence interval we make.

true

If your confidence interval is 95%, what is the value of Z that goes into the confidence interval formula?

1.96

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

Mu with subscript X-bar

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

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

A confidence interval for the mean is known as a range of likely values for the population mean.

true

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

-The mean of X-bar increases -Not enough information to tell -The mean of X-bar stays the same = ANSWER -The mean of X-bar decreases

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. = ANSWER -The standard error of X-bar stays the same. -The standard error of X-bar increases. -Not enough information to tell.

Bob wants a 95% confidence interval for the population mean. Previous research shows the population standard deviation is 8. He wants his margin of error to be no more than 4. What should his sample size be?

16

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

Suppose a pizza place claims it's average pizza delivery time is 10 minutes. Bob makes a 95% confidence interval for the average pizza delivery time for this pizza place and gets (15, 20). What does Bob think about the pizza place's claim?

He disagrees with the claim.

Bob makes a 95% confidence interval with a random sample of 100 and his margin of error is plus or minus 18. In order to cut the margin of error in half next time, what should Bob's sample size be? (Hint: You CAN determine the answer without knowing the standard deviation.)

400

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

-Statistics and parameters are the same thing -We use statistics to estimate or test parameters = ANSWER -We use parameters to estimate or test statistics

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

Suppose Bob makes a 95% confidence interval and his result is (70, 90). True or false: We can tell what Bob's sample mean must have been.

true

The margin of error increases if the sample size increases.

false

The margin of error of a confidence interval gets larger if the confidence level increases (assume all else stays the same.)

true