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
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
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.
Joon believes that 50% of first-time brides in the United States are younger than their grooms. She performs a hypothesis test to determine if the percentage is the same or different from 50%. Joon samples 100 first-time brides and 53 reply that they are younger than their grooms. For the hypothesis test, she uses a 1% level of significance. Need the p-value, and reject/fail to reject
p-value: .549, Fail to reject
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.
If p-value is greater than alpha level, researcher should fail to reject the null hypothesis.
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
Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 5% level of significance. State the null and alternative hypotheses.
Null: p = .92
Alternative: p < .92
the conclude step must mention what 3 things
1) determine if p-value is less than alpha level
2) reject or fail to reject null hypothesis
3) 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.
When you should use t-distribution for proportions
NEVER
Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 1% level of significance. Find p-value and reject/fail to reject.
P-value: .0046
Reject the null
Interpret a pvalue
The likelihood of getting your sample result or more extreme if the null is true
An M&M researcher wants to do a hypothesis test of the true proportion of yellow M&M's in a bag produced at the Cleveland factory at a .01 significance level
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 things should be included in the "STATE" step?
1) Null and Alternative Hypothesis
2) Significance level
According to the US Census there are approximately 268,608,618 residents aged 12 and older. Statistics indicate that, on average, 207,754 serious high school sports injuries occur each year (male and female) for persons aged 12 and older. This translates into a percentage of injuries of 0.078%. In Daviess County, KY, there were reported 11 serious injuries for a population of 37,937. Conduct an appropriate hypothesis test to determine if there is a statistically significant difference between the local injury percentage and the national inury percentage. Use a significance level of 0.01.
p = 0.00063
reject the null