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.