week 7 & 8 -- t-Distribution, df, CIs, hypothesis testing

Question 1

What is the problem with small samples?

Answer 1

ERROR (non-systematic difference btw estimator and paramter)

–> small samples are more likely to yield extreme results

Question 2

t-distribution

Answer 2

Used to make probabilistic inferences from small samples (instead of Normal)
paramters: df (or degrees of freedom), or “tail fattening”

Question 3

degrees of freedom (n - 1)

when estimating the population SD:

• Bessel’s correction corrects for BIAS
• the t-distribution corrects for ERROR

Answer 3

n = number of independent observations
df = number of independent observations...given any statistics we have already calculated for our sample

so if we have already calculated the mean, the last observation is not independent of the others (because we can calculate it…)

Question 4

another way to see sampling distribution

Answer 4

• we have a sample and have calculated its mean

- the sampling distrib. tells us what other means we might have got instead (for samples of this size, from this pop.)

Question 5

confidence intervals

Answer 5

?

Question 6

For each change, how does the CI change?

1. we want to be more confident (95% > 99%)
2. we take a larger sample
3. we study a larger population
4. we study a more variable population

Answer 6

1. wider
2. narrower
3. nothing
4. wider

Question 7

Which statement about the CI is correct for

85

Answer 7

5!

Question 8

Error bars

Answer 8

SD
- shows spread of sample
- usually widest
- doesn’t easily allow us to infer significant difference
SE
- related to the precision of our estimate
- narrowest
- doesn’t easily allow us to infer significant difference
CI
- DOES easily allow us to infer significant difference

Question 9

Good evidence is:

• probable given the hypothesis
• improbable otherwise

Answer 9

p value = P (D given NOT hypotehsis)

the probability of observing data as amazing as the data we have, given that our hypothesis is false