Week 6 Flashcards

1
Q

Degrees of Freedom & Shape of Chi-Squared distribution

A

D.O.F.#: of observations that are free to vary after sample mean has been calculated

Chi-Squared distribution: the chi-squared distribution is a family of distributions, depending on degrees of freedom:

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Sample variance & Distribution

A

X₁, X₂,…Xn is a random sample size “n” from a population with mean μ and variance σ²
_
The sample variance is defined as: = s² = Σ ( xi - x ) ²/ ( n - 1 )

s² varies from sample to sample, and therefore a random variable
The probability distribution of s² is the sampling distribution of the sample variance

The mean of the sampling distribution of “ “ s² is :E(s²)= σ²

The variance of the “ “ of “ “ s² is: Var(s²) = 2σ⁴/n-1

If the population distribution is Normal, then: (n-1)s²/σ² ~ X²n-1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Estimator v/s Estimate, Point and Interval estimates
(population parameters are often unknown and need to be estimated from the sample data)

A
  • Estimator: a tool that employs sample data to provide an approximation of an unknown parameter, takes the form of a random variable that varies from sample to sample
  • Estimate: specific value computed from a particular sample, it takes the form of a number or realized value of the random variable
  • a point estimate is a single number
  • a confidence interval provides additional information about variability

Width of confidence interval: lower confidence limit < point estimate < upper confidence limit

How well did you know this?
1
Not at all
2
3
4
5
Perfectly