AP Statistics: Confidence Intervals flashcards

Question 1

What is a confidence interval?

Accepted Answer

A range of values that estimates an unknown population parameter.

Question 2

What does a 90% confidence level mean for interval estimates from repeated samples?

Accepted Answer

About 90 out of 100 samples give an interval that contains the true population parameter.

Question 3

What is a point estimate?

Accepted Answer

One number calculated from sample data to estimate a population parameter.

Question 4

What is a parameter?

Accepted Answer

A numerical characteristic of a population.

Question 5

What does 'degrees of freedom' count in a sample?

Accepted Answer

The objects in it that are free to vary.

Question 6

How many degrees of freedom does a Student's t-distribution have for a sample of size n?

Accepted Answer

n - 1.

Question 7

Compared with the normal distribution, how does the Student's t-distribution look?

Accepted Answer

It has more spread and a flatter peak.

Question 8

What does the Student's t-distribution approach as n gets larger?

Accepted Answer

The standard normal distribution.

Question 9

Under what pseudonym did William S. Gossett publish the t-distribution in 1908?

Accepted Answer

Student.

Question 10

What is the general form of a confidence interval in terms of the point estimate and EBM?

Accepted Answer

(point estimate - EBM, point estimate + EBM).

Question 11

What happens to the error bound as the confidence level increases?

Accepted Answer

The error bound increases.

Question 12

What happens to the error bound as the sample size increases?

Accepted Answer

The error bound decreases.

Question 13

What is the EBM formula for a single population mean when the population standard deviation sigma is known?

Accepted Answer

EBM = z * sigma / sqrt(n), using the normal distribution.

Question 14

How is alpha related to the confidence level CL?

Accepted Answer

alpha = 1 - CL.

Question 15

How is the z-score z(alpha/2) defined?

Accepted Answer

The z-score that has an area of alpha/2 to its right.

Question 16

Which formula gives n for a target EBM when estimating a mean with known sigma?

Accepted Answer

n = z^2 * sigma^2 / EBM^2.

Question 17

Given only the interval's bounds, how do you get the error bound?

Accepted Answer

Take half the difference between the upper and lower bounds.

Question 18

Given only the interval's bounds, how do you get the sample mean?

Accepted Answer

Average the upper and lower bounds.

Question 19

When should the Student's t-distribution replace the normal for a mean interval?

Accepted Answer

When sigma is unknown and the sample standard deviation s is used to estimate it.

Question 20

What is the EBM formula for a single population mean when sigma is unknown?

Accepted Answer

EBM = t(alpha/2) * s / sqrt(n), where s is the sample standard deviation.

Question 21

How is the sample proportion p' calculated?

Accepted Answer

p' = x / n, where x is the number of successes and n is the sample size.

Question 22

What is q' in a proportion interval?

Accepted Answer

q' = 1 - p'.

Question 23

What is the error bound for a population proportion (EBP)?

Accepted Answer

EBP = z(alpha/2) * sqrt(p'q'/n).

Question 24

What is the confidence interval for a population proportion?

Accepted Answer

(p' - EBP, p' + EBP).

Question 25

In the 'plus four' method, how is p' calculated?

Accepted Answer

p' = (x + 2) / (n + 4).

Question 26

Which sample statistics are point estimates for mu and for sigma?

Accepted Answer

x-bar estimates mu, and s estimates sigma.

AP Statistics: Confidence Intervals flashcards

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