final review Flashcards
what are a and B
they are probabilities of Type I and Type II errors and NOT errors themselves
How can we control or minimize type one and type two errors?
with a fixed samples size, but not both at the same time. They are conflicting objectives that cannot be achieved simultaneously unless additional data are added by increasing the sample size
Ideally, how big would we like a and b to be?
as small as possible
Theoretically speaking, when the sample size becomes larger and lagers what happens
it reaches infinity and both a and B become 0, which is the smallest possible value. This is what happens when the sample is the WHOLE POPULATION
It is known that polygraphs (devices used to detect lies) may fail to detect whether a person is telling the truth or lies. suppose in one experiment with a polygraph, out of 250 persons who tell the truth, the polygraph indicates 23 are telling lies, and out of 200 persons who tell lies the polygraph indicates 19 are telling the truth.
What is the type I error
- construct the null and alternative hypothesis
HO; Person telling the truth
HA: person telling a lie
Type I error occurs when we decided to reject HO, thrive that Ho is in fact the true hypothesis.
in this case, it is the error committed when the polygraph indicates a person is telling lies when in fact they are telling the truth.
It is known that polygraphs (devices used to detect lies) may fail to detect whether a person is telling the truth or lies. suppose in one experiment with a polygraph, out of 250 persons who tell the truth, the polygraph indicates 23 are telling lies, and out of 200 persons who tell lies the polygraph indicates 19 are telling the truth.
What is the type II error
- construct the null and alternative hypothesis
HO: Person telling the truth
HA: person telling a lie
Type II error is committed when the polygraph indicates a person is telling the truth when in fact they are not
When sampling data support Ho, follow the practice of concluding by saying
do not reject Ho. this wording is weaker than “accept Ho” which should be avoided because of the risk of making a type II error
It is known that polygraphs (devices used to detect lies) may fail to detect whether a person is telling the truth or lies. suppose in one experiment with a polygraph, out of 250 persons who tell the truth, the polygraph indicates 23 are telling lies, and out of 200 persons who tell lies the polygraph indicates 19 are telling the truth.
a is the probability of a type I error. it is estimated by what and equals what
it is estimated by the relative frequency of persons who were telling the truth when the polygraph indicates they were telling lies.
23/250 = 0.092
It is known that polygraphs (devices used to detect lies) may fail to detect whether a person is telling the truth or lies. suppose in one experiment with a polygraph, out of 250 persons who tell the truth, the polygraph indicates 23 are telling lies, and out of 200 persons who tell lies the polygraph indicates 19 are telling the truth.
B is the probability of a type II error. it is estimated by what and equals what
B is estimated by the relative frequency
19/200 = 0.095
prob of persons were telling lies when the polygraph indicated they were telling the truth
The label on a 3-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.
a. Develop the appropriate null and alternative hypotheses. What is the Type I error in this situation?
b. What are the consequences of making this error? What is the Type II error in this situation?
c. What are the consequences of making this error?
Ho: M 1
a. Claiming M> 1 when it is not true
b. Claiming M
Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour.
a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour.
b. What is the Type I error in this situation? What are the consequences of making this error?
c. What is the Type II error in this situation? What are the consequences of making this error?
Ho: M >= to 220
Ha: M < 220
b. claiming M is <220 when it is not true
c. claiming M>= to 220 when it is not true
