L3

Question 1

What is the key concept to make inferences about parameters based on statistics?

Answer 1

Sampling distribution

Question 2

What is sampling distribution?

Answer 2

It is the distribution of a statistic taken as a random variable. So it is to take several random samples of a population and plot the results of the statistic (the thing you were looking for in the sample) in a frequency distribution. The curve which will appear is approximately a normal distribution if you took enough samples.

Question 3

What is random sampling?

Answer 3

It is the prerequisite for valid statistical inference. It is to take a random number of observations from the population.

Question 4

Central Limit Theorem

Answer 4

“The sampling distribution of the mean of a random sample drawn from any population is approximately
normal for a sufficiently large sample size n; the larger the sample size, the more closely it resembles a normal distribution.”

Question 5

What is the estimator and the estimand?

Answer 5

The statistic is the estimator and the estimand is the parameter

Question 6

Procedure of making an inference about the population variance

Answer 6

• obtain a number of equal-sized samples
• find the variance of each sample
• compute the distribution of the variance (Chi-squared distribution)

Question 7

sample variance notation

Answer 7

s^2

Question 8

What is a hypothesis

Answer 8

an educated guess

Question 9

research hypothesis

Answer 9

is our research goal. called H1

Question 10

Type 1 error = alpha

Answer 10

reject H0 if true

Question 11

Type 2 error = beta

Answer 11

do not reject H0 when it is false

Question 12

How are the error probabilities related?

Answer 12

They are inversely related. The higher alpha is the lower beta is.

Question 13

Which type of error is more serious?

Answer 13

Type 1 error (To reject H0 although it is true)

–> it is desirable to have a small alpha

Question 14

How does the hypothesis testing procedure start?

Answer 14

• It starts with the assumption that the null hypothesis is true
• the goal is to determine whether there is enough evidence to infer that the alternative hypothesis is true

Question 15

How can we gather evidence to reject or accept the null hypothesis?

Answer 15

• Calculating the relevant test statistic, e.g. the sample mean

Question 16

How do we know whether the test statistic provides enough evidence to reject or nor reject the null hypothesis?

Answer 16

1. Rejection region

2. p-value

Question 17

What is the significance level (alpha)?

Answer 17

It is the upper bound (the maximum tolerance) for the Type 1 error probability in a statistical test

Question 18

What is defined according to the significance level?

Answer 18

the extreme (rejection regions) are defined according to the significance level

Question 19

One-tail test

Answer 19

• rejection region is located in one tail of the sampling distribution
• alternative hypotheses involves either > or

Question 20

Two-tail test

Answer 20

• rejection region is set up so that we can reject the null hypothesis when the test statistic is too large or too small
• alternative hypothesis involves an inequality

Question 21

Which distribution do the one and two-tail tests use?

Answer 21

It uses the sampling distribution of the mean

Question 22

P-value

Answer 22

if P-value

Question 23

P-value two-tail Z test

Answer 23

sum up the probabilities of both tails