STUDY, STUDY, STUDY! Tomorrow's test is our most weighted test of the quarter!
Here's a breakdown of what's on your test:
- Conduct a hypothesis test! (hypotheses, conditions, math, conclusion! (ch. 20)
- Remember, if you are asked to "show statistical evidence," that evidence is the hypothesis test--all 4 parts!
- Also, remember that if you're given an alpha/significance level, this is a hint that it's a hypothesis test!
- Create a confidence interval! (conditions, formula with interval, interpret interval) (ch .19)
- Remember, if we have to "estimate a percentage" that means we have to create an interval--all 3 parts!
- Also, remember that if you're given a confidence level, this is a hint that you need to create an interval!
- Be sure you know how to use your graphing calculator to create intervals and conduct hypothesis tests! (one proportion z interval, one proportion z test)
- Know how to use a confidence interval to "test a claim" (ch. 21)
- Look to see if the value falls within your interval!
- Define Type I and Type II error, along with a consequence of each! (ch. 21)
- Remember, use the given info in the context when you identify the consequence--don't babble or go off on a tangent! Be concise!
- "In reality________, but our test_________."
- Know how the p-value compares for a one or two sided test (ch. 20/21)
- For example, if we conduct a one sided test and get a p-value of .033, what would the p-value have been if it were a two sided test?
- Find sample size given margin of error! (ch. 19)
- Know how changing alpha affects beta, and thus affects power! (ch. 21)
- Know how to identify alpha and beta when the rates of false positives and false negatives are given! (ch. 21)
- Definition of p-value (ch. 20)
- Know how changing our confidence level affects the width of an interval and margin of error (ch. 19)
- Know how changing sample size (n) affects the width of the interval and margin of error (ch. 19)
- Know the meaning of the confidence level! (ch. 19)
Here are some resources you can use to study!
- Look over your chapter 19 test!
- Want to practice a hypothesis test? Try this!
- Page 471: 17, 19, 21 (each of this is a test with the answers in the back of the book!)
- Try these problems from the unit review on page 513:
- Need practice with types of error? Look at the questions on the worksheet provided in class! Here are the questions/answers so you can check (answers in red).
Chapter 21: Types of Error
- In attempt
to increase the percentage of people wearing seat belts, Massachusetts
instituted a “click-it or ticket” policy. Use of safety belts rose to 62% in
2003, with a goal of surpassing 80% by 2005. That year (in 2005), of 134
stopped drivers, 23 were not wearing their seatbelt. Does this provide evidence
of meeting the goal? If we have met the goal, Massachusetts will cut back
funding on the “click-it or ticket” program.
a. Define each
type of error and a consequence of each.
Type 1: In reality, Massachusetts has not met it's goal of surpassing 80% of people using safety belts, but our test suggests they have met the goal. As a result, Massachusetts will cut funding on the "click it or ticket" program when they should not.
Type 2: In reality, Massachusetts has met its goal, but our test fails to show this. As a result, Mass. will continue to fund the "click it or ticket" program when they should not.
b. If we use
an alpha level of 0.05, what is the associated confidence level?
This is not on the test!
- A company
is willing to renew its advertising contract with a local radio station only if
the station can prove that more than 20% of the residents of the city have
heard the ad and recognize the company’s product. The radio station conducts a
random phone survey of 400 people.
b. Define a
Type I error and identify a potential consequence.
Type 1: In reality, 20% of residents have heard the radio station's ad, but our test suggests that more than 20% of residents have heard the ad. As a result, the company will renew its advertising contract when they should not have.
c. Define a
Type 2 error and identify a potential consequence.
Type 2: In reality, more than 20% of the city's residents have heard the ad, but our test fails to show this. As a result, the company will not review the advertising contract with the radio station when they should have.
d. Which alpha
level--.01, .05, or .10—will maximize the power of this test?
.10, because if we increase alpha, this decreases beta, which increases power (remember, power = 1 - beta)
e. The company
proposes the station call 600 people rather than 400. How will this affect the
power? Will this make the risk of a Type I/Type II higher or lower?
If we increase sample size, this decreases the probability of both type 1 and type 2 error (alpha and beta); thus, if beta decreases, power increases
- Testing for
Alzheimer’s disease can be a long and expensive process, consisting of lengthy
tests and medical diagnosis. Recently, a group of researchers devised a 7
minute test to serve as a quick screen for the disease for use in the general
population of senior citizens. A patient who tested positive would then go
through the more expensive battery of tests and medical diagnosis. The authors
reported a false positive rate of 4% and a false negative rate of 8%.
a. Define a
Type I error and identify a potential consequence.
In reality, a person should test negative (does not have Alzheimer's), but our tests shows they test positive (have Alzheimer's). As a result, the person will go through the more expensive battery of tests when they do not need to.
b. Define a
Type 2 error and identify a potential consequence.
In reality, a person does have Alzheimer's (should test positive), but our test fails to show this. As a result, this person will not go through the additional medical tests when they should have.
c. What is the
alpha level?
Alpha is the probability of a Type I error; a type 1 error is a false positive; so alpha = .04 or 4%.
d. Calculate
the power of this test?
Beta is the probability of a Type 2 error; a type 2 error is a false negative, so beta = .08. Power is 1 minus beta, so power = 1 - .08 = .92!
