Flashcards in statistics Deck (10):
three qualities of estimators
1. unbiased: expected value = population parameter
2. efficient: lower standard error than other estimators
3. consistent: as n increases, estimator approaches the value of the population parameter
what is most important quality of a sample?
central limit theorem
1. M(avg of means) = M
2. std error (avg of means) = std error
3. distribution of means approaches normal as n increases, regardless of distribution of population
standard error of the mean
standard error of the sample = standard deviation of individuals / sq root of n
null hypothesis sample testing:
1. state the Ho to be tested
2. specify the acceptable risk of a type I error
3. test, then find the probability (p-value) that a sample mean will differ from the true mean by a greater amount than found in the sample (remember to count extremes at both ends, unless one-tailed)
4. make a decision about Ho: accept or reject
used when std dev of population is known (which is rare)
z=(x bar - mu)/(std dev of x)
1-beta. the probability of correctly rejecting Ho when it is false.
used when std dev of population is not known. more common than z-test.
t=(xbar - mu)/(std dev of sample). use table to find t based on degrees of freedom.
assumptions of independent samples t-test
1. homogeneity of variance: variances in the population are the same (variance of X1 = variance of X2)
2. independent samples
3. random samples
4. normality: X1 and X2 are normally distributed in the populations