Lecture 2

Question 1

Parameters

Answer 1

describe the population e.g. population mean (mu_x), population variance (sigma^2) & population standard deviation (sigma)

Question 2

Statistics

Answer 2

infer the population e.g. sample mean (Xbar), sample variance (s^2) & sample standard deviation (s)

Question 3

What is a reasonable point estimate of the population mean?

Answer 3

sample mean

Question 4

How do we quantify the level of uncertainty of the point estimate (Xbar)?

Answer 4

interval estimation e.g. confidence level/confidence interval

Question 5

How do we figure out the sampling distribution of the point estimate (Xbar) to construct interval estimates?

Answer 5

central limit theorem

Question 6

What does the central limit theorem (CLT) tell us & what are its applications?

Answer 6

it tells us the distribution of our estimator & is used for hypothesis testing and to build confidence intervals

Question 7

What is a confidence interval & what is its formula?

Answer 7

it gives a range of values (e.g. [09, 14]) that is intended to cover the parameter of interest to a certain degree of confidence [insert image]

Question 8

What is the difference between standard deviation and standard error?

Answer 8

TBA

Question 9

review slide 9

Answer 9

in lecture 2 on ipad

Question 10

Confidence interval interpretation

Answer 10

we expect 95% of these interval to cover the true population mean (mu_x) and 5% do not

Question 11

The length of a confidence interval (CI) reflects…

Answer 11

our estimation uncertainty

Question 12

What does the length of a CI depend on?

Answer 12

population standard deviation (sigma), confidence level (1 - alpha) & sample size (n)

Question 13

review slide 18 & 19

Answer 13

in lecture 2 on ipad

Question 14

In practice, it is unlikely that sigma (population standard deviation) is available to us, what is reasonable solution to this dilema?

Answer 14

replace sigma with s (sample standard deviation)

Question 15

When using s instead of sigma how do we account for the added uncertainty?

Answer 15

use a slightly different sampling distribution that has fatter tails (student’s t distribution) [insert image]

Question 16

review slide 23

Answer 16

in lecture 2 on ipad

Question 17

What is hypothesis testing?

Answer 17

a method for using sample data to decide between 2 competing claims (hypothesis) about a population characteristic/parameter (e.g. mu)

Question 18

Null hypothesis

Answer 18

H_0, a claim about a parameter that is initially assumed to be true

Question 19

Alternative hypothesis

Answer 19

H_a, the competing claim

Question 20

What are the only 2 possible decisions in a hypothesis test?

Answer 20

reject H_0 & fail to reject H_0

Question 21

A statistical hypothesis test is only capable of demonstrating strong support for…

Answer 21

the alternative hypothesis, so be careful when setting up hypothesis

Question 22

What does rejecting the H_0 indicate?

Answer 22

strong support for the alternative hypothesis, H_a

Question 23

What does failing to reject the H_0 indicate?

Answer 23

lack of strong evidence against the null hypothesis, H_0

Question 24

Type I error

Answer 24

denoted by alpha, is when we reject H_0 even though H_0 is true

Question 25

Type II error

Answer 25

denoted by beta, is when we fail to reject H_0 even though H_0 is false

Question 26

A test statistic incorporates…

Answer 26

the sample size (n), the point estimate (Xbar), the standard deviation (s) & the hypothesized value (mu_0)