Samples, Proportions and Confidence Intervals Flashcards
How is a sample proportion distributed?
Few sample proportions at both extremes on the normal curve with the most being around the population proportion
The sample size affects the distribution
How to we determine the distribution of sampling proportions?
Calculate a Standard Error
____________
SE= | N (1-N) /
| n
N - Greek for pi - population proportion
n - sample size
Only used if sample size is over 30
Calculate a Z value - sample - population/ SE for proportion
Look at the table - gives you the area from the population proportion - looking at a half of the curve
Convert to % - 0.5 - area
How do we reject the null hypothesis?
We need to set a threshold
An alpha of 5% or 1%
If sample is in the greatest 5% then reject the null
When do we use confidence intervals?
When we don’t know a population parameter we estimate it from the sample - to give us greater confidence
What is a point estimate?
An estimate of a population mean
A sample mean in a random sample is not equal to the population mean
What is a confidence interval?
An interval for which we can say with a certain level of confidence that the value we are trying to estimate lies between 2 values.
95% and 99%
How does the distribution compare to the sample proportions?
Sample mean is placed in the middle
It should be close to the population mean
How do we calculate and what are the Z scores for 95% and 99% confidence interval?
Calculate the Z score by looking at half of 95
Gets a value of 1.96
A 99% CI will get us a value of 2.58
How do we calculate a 95% and a 99% confidence interval?
95% CI = (sample mean) +/- 1.96 x (SD/square root of n)
99% CI= (sample mean) +/- 2.58 x (SD/square root of n)
How do we compare CI of two statistics?
Use a Hi-lo plot
If they overlap there is no significant difference
How do we calculate CI with proportions?
___________
p +/- {1.96 x | p(1-p)/n }
What are some rules of CI?
We can use the sample SD as a reasonable estimate of the population SD if :
The data are normally distributed and we have a sample size greater than 30
