Confidence Intervals

Question 1

What is the p.d.f of the normal distribution?

Answer 1

Question 2

What is the special case for the normal distribution?

Answer 2

The standard normal N(0,1) with p.d.f

Question 3

What is the Central Limit Theorem?

Answer 3

Question 4

What is the Cental Limit Theorem for simple random sampling without replacement?

Answer 4

Question 5

Define a confidence interval.

Answer 5

A (1 - α) confidence interval for a population parameter θ, based on a sample from the population, is an interval which contains θ with probability (1 - α).

In the sense that if we repeatedly draw samples from the population and calculate an interval from each sample, thenm a proportion (1 - α) will contain the value θ.

Question 6

For large samples what is the formula for an approximate (1 - α) lvevl confidence interval for the population mean?

Answer 6

Question 7

When creating a confidence interval for the sample mean and we don’t know the standard error for the population what can we do?

Answer 7

Use the sample estimate of the standard error of mean.