9: Confidence intervals and the t-distribution

Question 1

What is a confidence interval?

Answer 1

For a parameter interval of numbers within which the parameter is believed to fall. The probability that this method produces an interval that contains the paramter is called the interval level. The number is chosen to be close to 1 - 0.99 or 0.95. Point estimate ± margin or error.

Question 2

What is the margin or error?

Answer 2

Z-score. Works as long as we have the standard deivation of the population distribution σ. y¯ ± z × σY

Question 3

What is a t-distrubtion?

Answer 3

Bell-shaped and symmetric about a mean of 0. Standard deviation is larger the 1 (extra error) and depends of the degrees of freedom. Gives flexibility - works for all sample sizes. Assumes - population distribution is normal.

Question 4

What are degrees of freedom?

Answer 4

Takes into account the constraints on the estimation process.

Question 5

Why are degrees of freedom limited in t-distributions?

Answer 5

Degrees of freedom are limited by the fact that for each example. The population variance has to be estimated, so only n - 1 quantities are free to vary in each sample.

Question 6

How do degrees of freedom influence t-distributions?

Answer 6

T-distributions has a diff spread for degrees of freedom. With larger degrees of freedom, the t-distribution gets closer to the standard normal, and is the same for the degree of freedom = 30.

Question 7

What is the problem with t-distributions?

Answer 7

If the population distribution is normal, them the sampling distribution is normal or any sample size too. But this does not work when the population distribution is not normal.

Question 8

What is the cental limit theorem?

Answer 8

For random sampling with a large sample size n (usually n = 30 is sufficient), the sampling distribution of the sample mean is approx a normal distribution.