Sample distribution; standard error; confidence interval; Using confidence intervals Flashcards
What are population parameters?
μ = population mean. σ^2 = population variance. σ = population standard deviation.
What are sample statistics?
The mean (M), variance (S^2), and standard deviation of a sample (SD/ S)
How can we learn about populations?
By using sample for inference about population
What is a disadvantage of samples?
Sample does not give true picture. It’s like seeing the
world through frosted glass.
how is the accuracy of samples affected?
- Multiple samples of same size (N) differ in their means
(even though all from same population).
-When we take infinitely many sample means we get
the sample distribution.
- Sample distribution is sometimes wide and sometimes narrow.
What forms a sample distribution?
multiple sample means form a distribution.
What is an advantage of narrower ditributions?
They are more sensible and offer greater trust
What forms a narrow distribution?
- Larger N (number of means) = narrower sample distribution.
(Law of Large Numbers). - Lower σ (population standard deviation) = narrower sample distribution.
(If σ = 0, every sample mean will be spot on)
What is a standard error (SE)?
The Standard Deviation of the Sample distribution
What does Standard Error (SE) represent?
SE reflects how far, on average, M (mean) is off the mark as an estimate of μ (population mean).
How to describe width of sample distribution?
Narrow sample distribution = M is trustworthy.
How do you calculate SE?
σ
SE = ——-
√N
What is the shape of sampling distributions and what is it based on?
Sampling distribution also has symmetric shape and is centred around μ.
How can you find σ (population standard deviation) to calculate Standard Error?
SD to estimate σ
Thus, we estimate SE as . SD/ √N
How can we increase the precision of our estimate?
To increase the precision of our estimate we can increase N (number of means).
