Data Analysis week 4

Question 1

What is the difference between a point hypothesis and an interval hypothesis

Answer 1

A point hypothesis is of the form statistic = value. An interval hypothesis is of the form statistic is in range …

Question 2

What is a condition for a hypothesis to be testable

Answer 2

It needs to be quantified

Question 3

What does hypothesis testing quantify

Answer 3

It quantifies how unusual the data is, assuming the null hypothesis is true

Question 4

What are the steps in hypothesis testing

Answer 4

You propose a number. You get a number as result of testing with a sample. You compare the proposed number to the resulted number out of tests. You search for evidence that the proposed number is not correct.

Question 5

What is the difference between the null hypothesis and the alternative hypothesis

Answer 5

The null hypothesis is often a point hypothesis and is interesting to reject. The alternative hypothesis is often the interval of everything but the value of the null hypothesis.

Question 6

What is a test statistic

Answer 6

A number calculated from the sample data used to compare test results with the expected result (null hypothesis).

Question 7

What happens when the data of the test results is consistent with the null hypothesis

Answer 7

Then you say “we failed to reject the null hypothesis”.

Question 8

What is the null distribution

Answer 8

The sampling distribution of the outcomes of a test statistic under the assumption that the null hypothesis is true.

Question 9

What is a p-value and what does it depend on

Answer 9

A p-value is the probability that a value at least as extreme as x is observed if the null hypothesis is true. It is the strength of the evidence that the null hypothesis is false. It is also a level of surprise about how surprised we are about the test results. The p-value is dependent on the null hypothesis and an observed sample statistic x.

Question 10

What does at least as extreme as mean (in a two sided test)

Answer 10

It means at least as different as the value of x from the value of the null hypothesis

Question 11

What is the significance level (alpha)

Answer 11

The criteria for rejecting the null hypothesis.

Question 12

When is the null hypothesis rejected

Answer 12

If the p-value is smaller than the significance level.

Question 13

What do you need to calculate the p-value

Answer 13

The null distribution

Question 14

How do you calculate the p-value

Answer 14

Create the null distribution by shifting the dataset so the null hypothesis becomes true. Create the sampling distribution of this dataset.