statistics

Question 1

three qualities of estimators

Answer 1

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

Question 2

what is most important quality of a sample?

Answer 2

randomness

Question 3

central limit theorem

Answer 3

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

Question 4

standard error of the mean

Answer 4

standard error of the sample = standard deviation of individuals / sq root of n

Question 5

NHST

Answer 5

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

Question 6

z-test

Answer 6

used when std dev of population is known (which is rare)

z=(x bar - mu)/(std dev of x)

Question 7

power

Answer 7

1-beta. the probability of correctly rejecting Ho when it is false. 
influenced by:
n
alpha
effect size

Question 8

t-test

Answer 8

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.

Question 9

assumptions of independent samples t-test

Answer 9

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

Question 10

independent samples t-test

Answer 10

(variance X1 + variance X2) / [(n1-1)+(n2-1)]