inference from one mean

Question 1

difference between inference for a mean and inference for a proportion

Answer 1

inference for a mean is more quantitative, continuous data while inference for a proportion is more categorical data.

Question 2

what is the parameter and point estimate for one mean

Answer 2

population mean mu

point estimate is sample mean x bar

Question 3

parameter for the mean of differences for two dependent groups

Answer 3

mu d

Question 4

parameter for the difference in the means of two independent groups

Answer 4

mu1-mu2

Question 5

central limit theorem

Answer 5

when we collect a sufficiently large enough sample of n observations from a population, the sampling distribution of xbar will be approximately normal

allows for normality condition to be relaxed

Question 6

two conditions for using central limit theorem and stating that xbar distribution is normal

Answer 6

independence
normality

Question 7

independence

Answer 7

observations must be independent from one another

Question 8

normality condition

Answer 8

when the sample is small, we require that the sample observations come from a normally distributed population

slight skew okay with 15+ observations
moderate skew okay with 30+
heavy skew okay 50+

if sample size is large, it can be relaxed

if sample size is small, no clear outliers, unimodal and roughly symmetric

Question 9

t distribution

Answer 9

accounts for added variability that occurs when we estimate the standard deviation with s(sample standard deviation) and standard error with s

• symmetric
  -bellshaped
• centered @ 0 with
  one parameter

thicker tails thats normal dis. (wider)

Question 10

t distribution parameter

Answer 10

degrees of freedom
degrees of freedom increase = distribution gets closer to normal distribution

n-1

Question 11

hypotheses examples

Answer 11

Ho: mu = muo. Ha: mu>muo
Ho: mu=muo. Ha: mu<muo
Ho: mu=muo. Ha:mu=/muo

Question 12

test statistic

Answer 12

t= (xbar-muo)/s/sqrtn

Question 13

confidence interval

Answer 13

xbar +- t* s/sqrtn

Question 14

as confidence level goes up, conf interval

Answer 14

also increases

Question 15

conf level

Answer 15

tells us how confident we can be that the interval we construct contains the one population mean

Question 16

t* vs z*

Answer 16

critical values of t-distributions are larger than z distributions because t-distributions have thicker tails

Question 17

confidence levels and hypothesis tests

Answer 17

both tests revolve around plausible/reasonable values of the population mean

a level significance hypothesis test rejects a hypothesis mu=muo for values of muo that fall outside of a level 100(1-sig level)% confidence interval for mu