Chapter 9 - Confidence Intervals

Question 0

Why are confidence intervals important?

Answer 0

Because they estimate parameters, without them there is no indication of precision
- intervals are often in the estimate +- margin of error

Question 1

What are confidence intervals?

Answer 1

States how often the interval covers the parameter value

Question 2

Confidence interval for a mean - known SD

Answer 2

If sigma SD (pop SD) is known, a level C confidence interval for mu (u) is
x-bar +- z*(sigma/sqr(n))

z* upper critical value of the standard normal

Question 3

For 95% CI

Answer 3

If x-bar is normally distributed, it will be within 2 SD’s (2sigma/sqr(n)) of 95% of the time so -

X-bar +- (2sigma/sqr(n)) covers mu (u) 95% of the time

Question 4

The margin of error gets _________ as C decreases, sigma decreases and/or n ______

Answer 4

Decreases

Increases

Question 5

CI for a mean - unknown SD

Answer 5

If the SD sigma (pop SD) is unknown we estimate it by the sample SD s ( sample SD) and a level C confidence interval for mu (u) is
x-bar +- t*(s/sqrt(n))

t* is the upper p critical value of the appropriate t distribution

Question 6

Characteristics if t-distributions

Answer 6

Similar to standard normal distributions with slightly heavier tails
-indexed by a parameter called degrees of freedom (df)

Question 7

Characteristics if df

Answer 7

Small df - heavier tails
Large df - lighter tails

Heavier tails means more likely to observe extreme observations - accounts for the extra uncertainty of know knowing sigma