Ch 14 - Introduction to Inference

Question 1

Significance tests
Someone makes a claim about the unknown value of

Answer 1

a population parameter

We check whether or not this claim makes sense in light of the “evidence” gathered (sample data).

Question 2

A test of statistical significance tests

Answer 2

a specific hypothesis using sample data to decide on the validity of the hypothesis.

Question 3

null vs alternative hypothesis

Answer 3

Question 4

One-sided vs. two-sided alternatives

Answer 4

Question 5

What determines the choice of a one-sided versus two-sided test is

Answer 5

1) the question we are asking and
2) what we know about the problem before performing the test.

If the question or problem is asymmetric, then Ha should be one-sided. If not, Ha should be two-sided.

Question 6

P-value:

Answer 6

The probability, if H0 were true, of
- obtaining a sample statistic as extreme as the one obtained or more extreme in the direction of Ha.

Question 7

small vs large p value

Answer 7

Question 8

P-values are probabilities, so they are always

Answer 8

a number between 0 and 1

area under curve (of extremes)

Question 9

The order of magnitude of the P-value matters more than

Answer 9

its exact numerical value.

Question 10

The significance level, α, is the

Answer 10

largest P-value tolerated for rejecting H0 (how much evidence against H0 we require).

This value is decided arbitrarily before conducting the test - it is a part of designing the test

Question 11

When the significance level, α, is ___ reject Ho

Answer 11

Question 12

To test H0: µ = µ0 using a random sample of size n from a Normal population with known standard deviation σ, we use the

Answer 12

null sampling distribution N(µ0, σ√n).

Question 13

The P-value is the area under N(µ0, σ√n) for values

Answer 13

of x̅ at least as extreme in the direction of Ha as that of our random sample

Question 14

To calculate the P-value for a two-sided test, use

Answer 14

the symmetry of the normal curve. Find the P-value for a one-sided test and double it.

Question 15

Answer 15

Question 16

Because a two-sided test is symmetric, you can easily use a confidence interval to test a two-sided hypothesis.

In a two-sided test,

C=

Answer 16

Question 17

A sample gives a 99% confidence interval of 0.83 - 0.85
With 99% confidence, could samples be from populations with µ =0.86? µ =0.85?

Answer 17

Question 18

A confidence interval gives a black and white answer: ____ But it also estimates a ____

Answer 18

Reject or don’t reject H0.

range of likely values for the true population mean µ.

99% sure true mean lies in interval

Question 19

A P-value quantifies how strong the evidence is against the H0. But if you reject H0, it ____

Answer 19

doesn’t provide any information about the true population mean µ.

Question 20

confidence interval vs test of significance

Answer 20

Question 21

Answer 21

Question 22

Answer 22