Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
16 Cards in this Set
- Front
- Back
|
Nominal/Categorical Data
|
It is not possible to calculate a sample mean so instead we can calculate the proportion of observations in the sample falling into a given category
|
|
|
Parameters
|
p = population proportion
q = 1-p |
|
|
Statistics
|
p hat = sample proportion
q hat = 1- p hat |
|
|
p hat =
|
number of successes in sample/n
|
|
|
Like sample mean, sample proportion can be viewed as ___________
|
a random variable
|
|
|
What we know about p hat:
|
- will have a mean equal to the population proportion (p)
- will have a variance equal to p x q/n - will be approximately normally distributed for large n (if n x p os equal to or larger than 5 AND n x q is equal to or larger than 5) |
|
|
What is the rule for proportions that determines if the data is approximately normally distributed?
|
n x p ≥ 5 AND n x q ≥ 5
|
|
|
Proportion notations
|
μ of p hat = p = mean of p hat
σ of p hat = √ (p x q)/n |
|
|
What is √ (p x q)/n
|
standard deviation or standard error of proportion
|
|
|
How is the confidence interval represented?
|
p hat + and minus Z x √(p hat x q hat)/n
|
|
|
When can the normal distribution (Z -score) be used?
|
If n x p ≥ 5 AND n x q ≥ 5 AND binomial conditions hold
|
|
|
Interpretation of CI for one proportion
|
I am 95 % confident that the proportion of Queenstown visitors who are Australian is between ____% and ______%
OR I estimate the proportion of Queenstown visitors who are Australian is _____% with a margin of error of ____% |
|
|
Formula for margin of error for a proportion
|
B = Z x √(p hat x q hat)/n
|
|
|
Solve for n:
|
n = Z² x p hat x q hat/B²
|
|
|
What do we do if the survey hasn't been conducted yet and we don't have p?
|
Use p= 0.5; this gives worst-case scenario (i.e. largest sample size to meet the margin of error requirement regardless of the proportion) and maximises function: f(p) = p(1-p)
|
|
|
n=
|
(Z x s/B)²
|
