Constructing Confidence Intervals

True or False: The more confident you want to be, the smaller your confidence interval will be.

• True

• False

Answer explanation

If I want to be more confident, the interval will have to be wider, leaving more room to be "wrong."

Margin of Error is equal to:

• Standard Deviation

• critical value * Standard Deviation

• Critical Value

• Point Estimate

What is the margin of error for the interval (6.8, 12.9)? (Hint, the point estimate is in the middle and then the same value [margin of error] is added or subtracted to it to get the upper and lower bounds)

• 9.85

• 3.05

• 3.50

• 6.8

Answer explanation

$point\ estimate\ \pm m\arg in\ of\ error$
The width of the interval is 6.1 (12.9 - 6.8).

Half of that is what is added/subtracted from the point estimate. (6.1 / 2 = 3.05) Therefore the margin of error is 3.05.

Which of the following is the confidence interval for the response "Bus?" (Hint: read all the information at bottom) Remember: CI=point estimate±margin of error

• (17.9, 24.1)

• (18, 24)

• (18, 36)

• (17, 24)

Answer explanation

 $point\ estimate\ \pm m\arg in\ of\ error$  
The point estimate for buses is 21% or 0.21.
The margin of error is listed as 3.1% or 0.031.

Lower bound: 0.21 - 0.031 = 0.179 or 17.9%
Upper bound: 0.21 + 0.031 = 0.241 or 24.1%

(17.9, 24.1)

Which of the following is an example of an interval estimate?

• point estimate 

• critical value

• confidence interval

• statistic

A __________ gives an interval of plausible values for the _____________. 

• confidence interval, statistic

• point estimate, parameter

• point estimate, statistic

• confidence interval, parameter

Complete the equation: 
point estimate +/- _____

• standard deviation

• margin of error

• critical value

• confidence level

Suppose that $51,759 was the median income for all households in 2012. Does the interval ($51,484, $52,394) provide convincing evidence that the median household income increased in 2013? 

• Yes

• No

What is the format for interpreting a confidence interval? 

• The interval from ___ to ___ captures the true mean in context.

• C% of samples of the same size taken from the same population will capture the parameter in question

• There is convincing evidence that C% gives the interval (___, ___) capturing the parameter in question.

• We are C% confident that the interval from ___ to ___ captures the [parameter in context].

What can you do to reduce the margin of error? 

• increase the confidence level

• decrease the confidence level

• increase sample size

• decrease sample size