Estimation

Question 1

When is Z used and what is the formula for Z?

Answer 1

-used if X is a continuous random variable with the general normal disrtibution with mean mew and variance σ^2

Question 2

formula for Z

Answer 2

(X-mew)/σ

Question 3

What is Xbar

Answer 3

an unbiased estimator of the sample mean- can be used when mew is unknown

Question 4

what is S^2

Answer 4

an unbiased estimator of the population variance

Question 5

how do you work out S^2

Answer 5

• look on pg 12 and 13 of the fb for the formula

- if given all the data then calc shows s so ou need to square that value

Question 6

Can you find the Standard deviation by rooting S^2

Answer 6

NO!! S^2 is an unbiased estimator of the variance σ^2 but not of standard dev σ because the expected value of a root of a variable is not equal to the square root of the expected value

Question 7

How to work out a confidence interval on a calc when standar dev is unknown

Answer 7

int-> t-> 1-s

now input the confidence level, s, x bar and n

Question 8

How to work out a confidence interval on a calc when standar dev is known

Answer 8

int -> z-> 1-s

now input the confidence level, standard devi, x bar and n