Sampling Distributions - Exam 1

Question 1

A random distribution of size n in a probability distribution is…

Answer 1

a sequence X1, X2, …, Xn of n independent variables all with that distribution.

Question 2

Sampling distribution

Answer 2

is a probability distribution for a statistic, ie for a function of the random sample - sample mean(Xbar), sample variance, sample proportion

Question 3

Xbar is this if X1,X2,…,X3 is a random sample for N(mew, sigma^2)

Answer 3

Xbar is N(mew, sigma^2/n)

Question 4

Central Limit Theorem Broad explanation

Answer 4

As the sample size increases, the sample distribution of the sample mean approaches a normal distribution.

Question 5

Central Limit Theorem Specific explanation

Answer 5

If we take any random sample X1, X2, … , Xn with any distribution with a mean mew and a variance sigma^2, then as n&raquo_space;> infinity, Xbar&raquo_space;> N(mew, sigma^2/n)

In practice, if n≥30, then Xbar is about N(mew, sigma^2)

Question 6

Special case for central limit theorem requires what? What does it entail?

Answer 6

Requires original distribution to be B(1, p). Then, Xbar if the proportion of success.

Question 7

Normal approximation to the Binomial distribution requires what?

Answer 7

for n large enough. rule of thumb: np ≥ 10, nq ≥ 10

Question 8

Continuity adjustment required when?

Answer 8

Discrete&raquo_space;> continuous

Question 9

Continuity adjustment

Answer 9

A discrete whole number c is represented by the interval [c-0.5, c+0.5)