Lecture 9: Confidence Intervals & Margin of Error Flashcards
Confidence interval (CI)
A range of values that we consider plausible for a parameter that we’re estimating
How to compute a CI
- Margin of error = critical point x estimated SEM
- CI = M +/- Margin of error
How to determine the critical point?
By the desired confidence level and the sample size
What is the CI for a population mean reported with?
the sample mean and sample standard deviation
What are some limitations of confidence intervals? (2)
- CIs only account for uncertainty caused by random sampling error, not any others
- We’re not guaranteed CI contains the true value of a parameter
When the sample size (n) is at least 30 or so then the critical point (CP) is usually ___ for a 95% confidence level
2
Basically we can approximate the 95% CI as M +/- 2SEM
The confidence interval is like what analogy?
A NET! –> In hopes that you capture the TRUE VALUE of the PARAMETER
To have a higher confidence level (To be more confident that your net captures the true value of the parameter) then the CONFIDENCE INTERVAL must be ______?
Wider!! (You need to cast a wider net)
The estimated SEM is a generic unit of ______?
UNCERTAINTY
To determine the confidence interval (actual wiggle room around the estimate) requires deciding on a _____ ____, which determines how many _____’s we need around the estimate
confidence level
SEMS
CI’s only account for uncertainty caused by what type of sampling error?
random sampling error
CI’s account for uncertainty caused by random sampling error but not other types of errors like? (4)
- Biased sampling
- Fraud
- Incorrectly recorded measurements
- Computation mistakes
Is it ever guaranteed that the CI contains the true value of the parameter?
NEVER - we won’t know if the CI we computed is one the 95% or one of the 5%
sample mean (M) is just an estimate so for the population (mew) we have to leave some ____ ____ around our estimate to account for _______ ______
Wiggle room
Sampling error
For a given estimation of a parameter, a 99% CI will be ____ than a 90% CI
Wider
For all CIs you compute at the 95% level, ____% of them will contain the true value of the parameter and ___% won’t
95
5
In 2.5% of CI’s the upper bound will be ____ the parameter value
below
In 2.5% of CI’s the lower bound will be ____ the parameter value
above
For a:
- sample mean (M) of 80
- 95% CI
- Lower bound of 76.1
- Upper bound of 83.9
- SD of 5
How would you write that out in the correct format?
M = 80.0, 95% CI = [76.1,83.9], SD 5.0
