FM Stats U5 Flashcards
Define central limit theorem
If a random variable X has a mean and finite variance (u, s^2) , whatever its underlying distribution, the distribution of the sample mean Xbar may be approximated by a normal distribution (u, s^2/n) if n is sufficiently large (>30)
What is an estimator?
A sample statistic chosen to estimate a population parameter.
What is the standard error?
The standard deviation of an unbiased estimator
Unbiased estimator for variance S^2
1/(n-1) (sum(x^2) - n(xbar)^2)
Define significance level
The probability of the thing being in the critical region, P(type 1 error)
What does the p-value represent?
The probability that the observed result or a more extreme one will occur under H0.
How does one interpret a p-value?
p < 0.01 very strong evidence to reject H0
0.01 < p < 0.05 strong evidence
p > 0.05 insufficient evidence
How does one interpret a p-value given significance level?
p > SL insufficient evidence
p < SL sufficient evidence
What is the critical region?
The set of values of X for the number of successes that would result in rejecting H0
What is the mean test statistic for normal distrubutions?
z = (Xbar - mu) / (sigma/sqrt(n))
What is the formula for the difference between two means?
z = ((x1bar - x2bar) - (mu1 - mu2)) / sqrt(sigma1^2/n1 + sigma2^2/n2)
Give the two assumptions made for normal hypothesis tests
- The s.d. of the parent is known
- The underlying distribution is normal
What is the degree of freedom of a student’s t?
sample size - 1
Define a P% confidence interval
A P% confidence interval means that P% of intervals constructed from samples of the same size will include the true value of the population parameter under consideration.
Confidence interval formula for normal?
CI for mu = Xbar +- ksigma/sqrt(n)
