8. Confidence Intervals Flashcards
What are confidence intervals?
Confidence intervals are constructed at a confidence level, such as 95 %, selected by the user.
It means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95 % of the cases. (A confidence stated at a 1−α level can be thought of as the inverse of a significance level, α.)
How do we form confidence intervals?
The purpose of taking a random sample from a lot or population and computing a statistic, such as the mean from the data, is to approximate the mean of the population.
How well the sample statistic estimates the underlying population value is always an issue. A confidence interval addresses this issue because it provides a range of values which is likely to contain the population parameter of interest.
One sided and 2 sided confidence intervals
In the same way that statistical tests can be one or two-sided, confidence intervals can be one or two-sided.
A 2 -sided CI brackets the population parameter from above and below. A 1-sided CI brackets the population parameter either from above or below and furnishes an upper or lower bound to its magnitude.
What are the population parameters for confidence intervals?
mu=mean
pi=proportion
What is a sample statistic?
A point estimate (single number):
mean=xbar,
Proportion =p
What do confidence intervals do?
give extra info using the variability of the estimate + the upper and lower confidence intervals
What can we do with a point estimate (population statistic) & its sample mean & proportion?
we can estimate a population parameter
Meaning of confidence intervals
in practice, you only take one sample of size n. You don’t know mu, so you don’t know if the calculated interval actually contains mu. BUT you do know that 95% of samples will give an interval containing mu.
basic formula for confidence interval
= point estimate +- (critical value)* standard error
Once you’ve estimated the mean value through a confidence interval of a sample, how do you estimate the total of that, what do you do?
Multiply the confidence interval by (the population number)
what are the assumptions necessary to utilise the t-function?
data is continuous, data when plotted follows normal distribution, reasonably large sample size is used,
The distribution of the sample proportion is approximately normal if….
npi>=5, n(1-pi)>=5
