Quantitative - Involves numbers, denoted by x-bar and used to predict μ (population parameters)
Qualitative (categorical) - Involves objects other than numbers (e.g. hair color or gender), denoted by p-hat and used to predict P (proportion parameters).
In Class Skittles Exercise
Each student was given a fun size package of skittles and asked to record:
1) Total number of skittles
2) Number of purple and red skittles (combined)
3) Proportion of skittles per package that are red and purple (combined)
The total is quantitative (number)
The proportion is categorical because it's a color reported.
Sample size = 36 students in the class
Normally distributed - Average number of skittles per package 16
X-bar (mean): 15.125
Standard deviation: 1.328
If you are asked to report your mean? Just report the number of candies present in your bag.
Although better estimates come from taking larger sample sizes or taking more samples.
Central Limit Theorem (CLT) for Means (x-bar) - Allows us to figure out how samples of varying sizes behave in the long run.
The Central Limit Theorem states that:
1) Shape: Is normal or approximately normal
2) Center: μ(subscripted x-bar) = μ, meaning the center for both the population and the sample is the same.
3) Spread: σ(subscripted x-bar) = σ/√ n (standard deviation divided by the square root of the sample size)
Note: We can only use the CLT when n ≥ 30 or the population is normally distributed
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