chapter 17: tests of significance

Question 1

to assess the evidence provided by data about some claim concerning a population parameter, you _____

Answer 1

use a test of significance

Question 2

null hypothesis H₀

Answer 2

The claim tested by a statistical test of significance is called the null hypothesis. The test is designed to assess the strength of the evidence against the null hypothesis. Usually the null hypothesis is a statement of “no effect” or “no difference.”

Question 3

significance tests, in a nutshell…

Answer 3

an outcome that would rarely happen if a claim were true is good evidence that the claim is not true

Question 4

alternative hypothesis

Answer 4

The claim about the population that we are trying to find evidence for is the alternative hypothesis. The alternative hypothesis is one-sided if it states that a parameter is larger than or smaller than the null hypothesis value. It is two-sided if it states that the parameter is different from the null value (it could be either smaller or larger).

Question 5

P-value

Answer 5

The probability that measures the strength of the evidence against a null hypothesis. Small P-values are evidence against H₀ because they say that the observed result would be unlikely to occur if H₀ were true. Large P-values fail to give evidence against H₀

Question 6

H_a

Answer 6

The alternative hypothesis, which sets the direction that counts as evidence against H₀.

Question 7

“Significant” in the statistical sense

Answer 7

“Significant” in the statistical sense does not mean “important.” It means simply “not likely to happen just by chance.” Significance at level 0.01 is often expressed by the statement, “The results were significant (P < 0.01).”

Question 8

Significance at level a

Answer 8

If the P-value is as small, or smaller than, α, we say that the data are statistically significant at level α. The quantity α is called the significance level or the level of significance, and is often .05 (1 in 20 that a sample would give evidence this strong just by chance) or .01 (1 in 100).

Question 9

Whenever P-value < α

Answer 9

we ca reject the null hypothesis

Question 10

Why should you always check the conditions as the first step in the solve portion of the four-step process

Answer 10

There is no point in computing the test statistic and finding the P-value if the conditions are not met.

Question 11

We always express hypotheses in terms of __________.

Answer 11

Hypotheses are claims about population parameters, never sample outcomes

Question 12

If P-value > α, the decision we make is to ___________________

Answer 12

FAIL TO reject the null hypothesis

Question 13

What does statistically significant mean in a test of hypotheses?

Answer 13

not likely to happen due to chance… Significant means that the difference between the observed sample statistic and the claimed parameter value is too BIG to be due to chance.

Question 14

What should you include in the interpretation of a P-value?

Answer 14

1. the probability is about getting the sample statistic
2. the assumption is on the null hypothesis being true

Question 15

An outcome that would rarely happen if a claim were true is good evidence that the claim is ___________.

Answer 15

not true

Question 16

In a test of significance we make a claim and ask if the data give evidence ____________ it.

Answer 16

against

Question 17

Suppose we are testing H0: μ = 50 versus Ha: μ > 50. Which mean will have the smallest P-value?

Answer 17

The one furthest from 50