- For 1B, your task is to figure out the confidence level based on our alpha level--we'll get into this some more tomorrow! For now, do your best! Or, check p. 479-480 about critical values!
- For 2d and 2e, you are asked how the power and risks of Type I/II error are affected--use the flow chart I provided in class!
- Also, know that as we increase alpha, beta decreases!
- For 3cd, remember that alpha is the probability of a type 1 error and beta is the probability of a type 2 error...
- These probabilities are given: try to remember, false + is which type? false -?
- Remember, power = 1 - beta.
Here are the homework questions in case you don't have a copy:
Chapter 21: Types of Error
1.) 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.
b. If we use
an alpha level of 0.05, what is the associated confidence level?
2.) 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.
a. Write the
hypotheses.
b. Define a
Type I error and identify a potential consequence.
c. Define a
Type 2 error and identify a potential consequence.
d. Which alpha
level--.01, .05, or .10—will maximize the power of this test?
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?
3.) 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.
b. Define a
Type 2 error and identify a potential consequence.
c. What is the
alpha level?
d. Calculate
the power of this test?
Homework Answer Key (will be provided in class tomorrow):
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