Confidence Intervals Flashcards
What is a confidence interval for a population mean
Remember any confidence interval is based on a confidence level
An interval constructed around the sample mean so we are reasonable sure that it contains the population mean
n = 50
Sample mean = 31.56.
The 95% CI
X +- 1.96(sd) = x +- 1.96 sd/sr n
The probability that the comfidence interval will contain the population mean is shown by what symbol
1 - æ is referred to as the confidence coefficient
(1-æ) x 100% is called what?
The confidence level
If a population has a standard deviation (known) and if the population is normal or if the sample is large (n>30), then
a (1- æ)100% confidence interval for the mean is the formula for 95% CI
Now if the standard deviation is unknown (usually) we can construct a CI for the mean by using what formula?
t-based confidence intervals
t= x- u / s/ sr n
The curve of this distribution is similar to the standard normal curves
- symmetric and bell shaped
- more spread out than the standard normal distribution
The t distribution
The spread of the t is given by what?
The number of degrees of freedom
What is the size comparison with the sample n and the degrees of freedom
For every sample n there is one fewer degrees of freedom
df = n-1
right hand tail is what on the t distribution?
tæ is the point on the horizontal axis under the t curve that gives a right hand tail to æ
So the value of the tæ depends on the right hand tail and the number of degrees of freedom
Population proportion- of the sample size is large then (1-æ)100% CI for p is
P +- zæ/2 se p(1-p)/n
To do this n should be considered large if:
n*p >_ 5
n*(1-p)>_ 5
Finite population and a strong sample n> 30 (5% or higher of a sample of the population)
Then add onto the formula a calculation for finite population which is
N-n/N-1
