REVIEW: What is a population parameter?
A value related to a population that can really only be found via estimation using sample statistics
What is a confidence interval?
The interval used to estimate a population parameter
What is Hypothesis testing?
(What is its objective?)
To determine whether or not the given data supports or contradicts the claims made about a population parameter
How do we estimate a population mean?
We use confidence intervals based on the sample mean and sometimes the sample variance
What does the value ‘E’ represent in hypothesis testing?
The error
Ex: What does a confidence level of 90% mean?
90% of repetitions contain μ within the margin of error
90% chance for μ to fall inside the margin of error
AND 10% OUTSIDE
How do we construct a confidence interval?
Sample mean - Error < μ < Sample mean + Error
What does it mean if X HAT (sample mean) is WITHIN a value?
That value is E (the margin of error)
When is σ (population standard deviation) used and when is S (sample variance) used for confidence intervals?
σ : Must be given
S: Can be calculated, therefore can be used when σ is unknown.
-> Population can be normal and non-normal for both
What does a higher Confidence Level indicate?
Confidence interval is wider, answer is less precise, more likely to contain population mean
What does a large sample size indicate? (3)
A lower standard error and a narrower interval of confidence (more accurate values). Sample mean approaches population mean.
What does a lower Confidence Level indicate?
Confidence interval is more narrow, answer is more precise, BUT less likely for population mean to be inside
What happens when n<30 and σ unknown??
Must use t-distribution (chapter 11)
