Unit 9: Testing a Claim

p-value

Probability, computed assuming Hₒ is true, the statistic would take a value as extreme as or more extreme than the one actually observed.

interpreting p-values

small p-value (p

Conclusion when p

Because p

Conclusion when p>α

Because p>α, we fail to reject the null hypothesis.

At the \[__α]__% level of significance, there is not enough evidence to support the claim that __[alternative/claim]__.

Null and Alternative Hypothesis

Null: rejected or not

Alternative: supported or not

Type I and Type II Errors

Type I: You reject the null, but what if it was true?

* p(type I) = α

Type II: You fail to reject the null, but what if it was false?

* p(type II) = 1-power

Conditions for significance test about a proportion

(p is from null hypothesis, not p̂ )

Test statistic for proportions

z score

power

The probability that the test will reject Hₒ at a chosen significance level α when the specified alternative value of the parameter is true.

* higher power is desirable

Ways to increase power:

* increase α
* consider an alternative farther away from the original p
* increase the sample size
* decrease σ (by improving measurement process or restricting attention to a subpopulation)

Conditions for significance test about a mean

10% not necessary if we aren’t sampling

normal/large sample:


1. is the population distribution normal?
2. is n >= 30?
3. is there any strong skewness or outliers? (sketch a graph)

test statistic for means