inference for paired data (mean of differences

Question 1

what does examining the differences between two measurements on one individual do?

Answer 1

we eliminate the variability across individuals
we control for one source of variation

Question 1

data are paired when

Answer 1

there is each observation in one data set corresponds to exactly one observation in the other data set

two measurements on each individual in the sample

we are interested in the differences within each pair

Question 2

what is our parameter of interest

Answer 2

mu d populaition mean of differences

Question 3

what is the point estimate for mu d

Answer 3

xbar d the sample mean of the differences

Question 4

what conditions of the sampling distribution xbar d are required to be met for the distribution to be normal

Answer 4

independence
normality

Question 5

independence

Answer 5

the observations within the sample of differences are independent

Question 6

normality

Answer 6

small —> look at outliers and shape of histogram etc.

central limit theorem -> relax for large sample sizes

Question 7

hypotheses equations

Answer 7

Ho: mu d = 0
Ha: mu d =/ 0