General Ideas
What are we trying to estimate with a confidence interval?
The population average, u
What type of sample must we take to use confidence intervals?
A simple random sample
When would we use a z interval instead of a t interval?
1. The population standard deviation is known
2. Sample size is large
(The opposite requirements are for the t interval)
Definition: Using a sample to infer about an unknown population average.
Inference
What is the best estimator of the population average?
The sample average.
What can we not have in our sample in order to do a confidence interval?
Outliers
What is the last step when calculating a required sample size?
ROUND UP
If we created 700 confidence intervals all at 60% confidence level, how many would we expect to not capture the true average?
700 * (100%-60%) = 280
What should we do if we want to create a larger margin of error?
1. Decrease the sample size
2. Increase the confidence level
For a sample size of 5, what shape must the distribution be?
Bell shape
Find the critical value, z* for a 70% confidence interval.
1.0
What is the equation for the margin of error?
ME = (z*s/sqrt(n))
True or False:
If a guess of the population average is greater than our lower bound and less than our upper bound, we say that it could be correct.
True.
If the guess is inside the confidence interval, it could be correct.
For a sample size of 29, what shape must the distribution be?
Symmetric
Find the 60% confidence interval for the following information:
sample average = 6
sample standard deviation = 1
sample size = 50
(5.9, 6.1)
What would be the confidence interval with a confidence level of 0%?
What theorem allows us to do confidence intervals?
The central limit theorem [not on QLT]
For a sample size of 200, what shape must the distribution be?
Anything
True or False:
If we consider all possible 80% confidence intervals arising from all possible samples of the population, then 80% of those intervals should contain the population average.
FALSE
If we consider all possible 80% confidence intervals arising from all possible samples of the same size of the population, then 80% of those intervals should contain the population average.
What would be the confidence interval with a confidence level of 100%?
(-infinity,+infinity)