What is a Test of Significance?

< p-value test

left tail test

significant

not likely to happen just by chance

p-hat

observation

two-sided alternative

statement that mu or proportion is not equal some value.

smaller/stronger

the __________ the P-value is, the __________ is the evidence against H0 provided by the data.

one-sided alternative

the effect we seek evidence for says that the population proportion is greater than one-half; statement that mu or proportion is greater than or less than (> or <) some value.

P-value

the probability, computed assuming that H0 is true, that the sample outcome would be as extreme or more extreme than the actually observed outcome; how well the and the null hypothesis agree.

not equal to p-value test

two tail test

test of significance

A test to assess the evidence provided by data against a null hypothesis H0 in favor of an alternative hypothesis.

statistical significance

If the P-value is as small or smaller than α, we say that the data are statistically significant at level α.

alternative hypothesis

The claim about a population that we are trying to find evidence for is the alternative hypothesis, written Ha; can be one-sided or two-sided.

statistical tests

ask if sample data give good evidence against a claim

standard score

calculated by subtracting the mean from the observation and dividing it by the standard deviation.

sampling distribution

can be a mean (mu) or a proportion (p) - need to recognize which one you are dealing with; will always be normal; if dealing with mean, the mean = mu and the standard deviation = sigma/the square root of n; if dealing with a proportion, the mean = p and the standard deviation = the square root of p(1-p) divided by n.

5%

cut off point for p-value; < is too small (null hypothesis NOT true) and > is just right (null hypothesis IS true)

> p-value test

right tail test

significance level

The significance level, α, is the test's probability of a Type I error.

null hypothesis

The statement being tested in a statistical test is called the null hypothesis H0. Usually the null hypothesis is a statement of "no effect" or "no difference"; statement that mu or proportion equals (=) some value.