Significance Test Basics
The part of your hypothesis that is the claim someone made.
The null
The type of error you could have when you fail to reject the null when you really should have rejected the null
Type II
The name of the method used to perform a significance test for proportion
one sample z-test for p
Identify three (out of 4) things that should be included in the "STATE" step
1) Hypotheses; 2) Significance level; 3) Initial evidence of Ha (sample mean); 4) define parameter p1-p2
If the alpha level is .05 and the pvalue is .051, what conclusion do you make?
The type of error that could occur when you reject the null when you should have failed to reject the null.
Type I
The three things you need to do in the "DO" step when performing a significance test for proportion
1) Find the test statistic (z-score) using equation
2) Find the p-value from the table
3) Determine if you should double the p-value based on whether Ha is two sided.
The name of the method used to perform a significance test for difference in proportions
two sample z-test for p1-p2
what we know about our p-value if the Ha has a "not equal to" symbol
it is two sided and we must double the p-value.
A researcher conducts a one-sample z-test for proportion and finds a p-value of 0.07. What type of error could he have made at the alpha=0.05 level. Explain how you know.
This means researcher could could have made a Type II error.
This is how we check the normal condition for tests with proportions
LCC:
np0 and n(1-p0) are at least 10
How to verify the normal condition when using a two sample z test
Do the large counts for both sample sizes using combined proportion OR use p^c = (p^1+p^2)/(n1+n2), then n1(p^c)>=10; n1(1-p^c)>=10; n2(p^c)>=10; n2(1-p^c)>=10
the conclude step must mention what 2 things
1) determine if p-value is less than alpha level
2) reject or fail to reject null hypothesis
or
Indicate if have convincing evidence for Ha in CONTEXT
A new cancer screening test is supposed to detect cancer at the alpha=0.01 level. What would an example of Type I and Type II error be with the machine? Which is more serious?
Type I: Reject null wrongly. This would mean the machine identifies cancer when patient does not have it. (False positive)
Type II: Fail to reject null wrongly. This means machine fails to identify cancer when it should have. (False negative)
Type II is more serious because patient could die.
What is the combined p? Why do we use it?
p^c) = (p^1+p^2)/(n1+n2)
We use it to assume "no difference" or p1-p2 = 0 between two proportions.
Standard Deviation of two sample z test
Square root of : p^c(1-P^c)/ n1 + p^c(1-P^c)/n2
Interpret a pvalue
The likelihood of getting your sample result or more extreme if the null is true
An M&M researcher wants to compute the 99% confidence interval of the true proportion of yellow M&M's in a bag produced at the Cleveland factory.
What is the probability the researcher commits a Type I error?
.01 or 1%
The prob of a Type I error is equal to the alpha level. The alpha level is 100% minus the confidence level(99%).
The Mars Candy Company claims M&M's produced at their Cleveland facility contain 20% blue M&M's. You believe that the proportion of blue is actually less than that. If 100 M&M's are chosen at random and 16 are blue, calculate the test statistic (z), the p-value, and determine if there is convincing evidence at the alpha=.05 level that the true proportion is less than they claim.
hatp=16/100=.16
z=(.16-.20)/sqrt(((.2)(.8))/100)=-.04/.04=-1
p value = .1587
Fail Reject
The standardized test statistic for a test of Ho: p = 0.4 versus Ha: p not = 0.4 is z = 2.43. Determine the result for an alpha 0.05 and a result for an alpha 0.01
Significant at alpha 0.05 but not significant at alpha 0.01
Reject at 0.05, fail to reject at 0.01