Confidence Intervals for Population Mean (5/7) Final Exam

because bigger interval and more values

as confidence level increases, z* increases, and MOE increases -why?

decreases

as sample size (n) increases, MOE

a more diverse population makes it harder to pinpoint the mean

as standard deviation of the population mean increases, MOE increases...why?

1. sample size 2. population SD 3. confidence level

3 things that affect MOE

1.645

90% confident: +/- ______ standard errors

How to Answer

We are 95% confident that the {} is between {} and {}

Mu with subscript X-bar

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

Confidence interval for the population mean

When you are asked to provide a range of likely values for the average gas price in Columbus Ohio, what technique do you use?

We use statistics to estimate or test parameters

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

The mean of X-bar stays the same

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

#

statistical conclusion

2.58

99% confident: +/- ______ standard errors

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

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

Sampling distribution of X-bar

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

stay the same

if the sample mean was 15 years instead of 10, what would happen to MOE? (because MOE and X-bar are not related)

n>30

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.)

X-bar is approximately normal if n > 30

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 exactly normal for any n

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

increase confidence level

Which of the following would increase the Margin of Error?

answer in common language

contextual interpretation

middle

whenever we are given confidence interval with z, it's always in the

1.96

95% confident: +/- ______ standard errors

increase it by 16 times what it was before

Suppose you found a 95% confidence interval for the mean using a random sample of size n, and you found it was too wide; that is, the margin of error was too large. If you wanted the margin of error to be ¼ of what it was before, what do you have to do to the sample size? (because of the square root)

n>30

since the formula for the confidence interval of a population mean uses z, we have to treat X-bar like it's normal so

statistic

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:

True

(T/F): The margin of error of a confidence interval increases if the population has a higher standard deviation.

true

(t/F)" If everything else stays the same, a 90% confidence interval is narrower than a 95% confidence interval.

z*

critical values

confidence interval

range of likely values for the parameter

Yes - a larger n always reduces MOE

can you have a high confidence level and a small MOE? why?

Yes

If your 95% confidence interval for the average gas price in Columbus Ohio turned out to be ($2.25, $2.75), do you know what the sample mean was?

The standard error of X-bar decreases.

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

Likely

a confidence interval provides a range of ______ values for a population parameter (such as population mean)