Transcript Document

Pizza Delivery
• Pines Pizza claims that on average
they deliver in 20 min or less.
• Design an experiment to test their
claim.
• Remember your three principles of
experimental design( control,
replication, randomization.
• What would constitute sufficient
evidence that they are wrong in their
claim.
• Your group has 15 minutes.
Mr. Pines says that his twelve round washer
score average is at least 40 pts. Coach
Enright says, “no way”. Coach Enright
decides he will run some tests on this
situation.
• Ho : μ = 40 vs. Ha : μ < 40, where
μ is the mean average of Mr.
Pines twelve inning washer
score.
Rejecting the Ho
• Determine what should be done
with the following P-Values
1.P(Z < -1.43)
= 0.0764, reject at the 10% level
1.P(Z > .34)
= 0.3669, do not reject Ho
1.P(Z ≠ 2.87)
=
0.0041, reject at the 1% level
Is it Significant?
(a) Mean = 536.7
P-Value = .0505 Do not reject Ho
(b) Mean = 536.8
P-Value = .0496 Reject at 5% level
(c) The sample mean only changed by a
tenth, slight variation completely
reversed our conclusion
Sample size and p-value
(a) n = 100 P-Value = .3628 not
even close to rejecting null
(b) n = 1000 P-Value = .1336 not
enough to reject null
(c) n = 10,000 P-Value = .0002
reject at any level
Is the die fair?
• Roll the die you were given 50
times, keep track of all rolls.
• A fair die has a mean μ = 3.5 and
standard deviation σ = 1.71.
• Is there significant evidence at the
5% level based on your rolls that
the true average of the die is not
3.5?
• Show all work
Back to the Real Die
Recall that a real die has μ = 3.5
and σ = 1.71….last week we
rolled the die 50 times.
What sample mean would we
need to get in order to reject
the null(μ = 3.5 ) at the 5%
level?
What does P-Value
mean?
• P-value assumes Ho is true.
• It is a percent.
• It is the probability of your sample
happening by chance if Ho is true.
Type 1 and 2 errors
• Type 1 error — Rejecting Ho when
it’s true.
• Type 2 error — Failing to reject Ho
when it’s false.
Type I and Type II errors
Which type of error is more
serious? …. You have to read
the problem!
Decreasing the chance of a type I
error increases the chance of a
type II error…and vice versa
Type 1 and 2 errors
• What is the probability of that error?
• Type 1 is the alpha level.
• Type 2 is β and complex and you do not
have to know.
• What is power?
• Power = 1 - β
It is the probability of correctly
rejecting Ho when it is false.
Type 1 and 2 errors
• Ho: the space shuttle is safe—launch
rockets.
• Ha: the shuttle is not safe. Do not launch
rockets.
• What is a type 1 error and its
consequence?
• What is a type 2 error and its
consequence?
• Which is worse?
• Draw this situation in a two-way table.
A quality inspector plans to test a sample of
40 bottles of soft drink labeled as 20 ounces.
If she finds the mean content to be less than
19.8 ounces, she will have the bottling
machinery stopped and recalibrated. If it is
known that the machine operates with a
standard deviation of 0.75 ounces, what is
the probability that the inspector will
mistakenly stop a machine that is delivering
a mean of at least 20 ounces per bottle?
(A) .023 (B) .046 (C) .050
(D) .092 (E) .119
B
Which of the following statements are true?
I It is helpful to examine your data before
deciding whether to use a one-sided or
two-sided hypothesis test.
II If the P-value is 0.05, the probability that
the null hypothesis is correct is 0.05.
III The larger the P-value, the more evidence
there is against the null hypothesis.
(A) I only
(B) II only (C) III only
(D) II and III
(E) None of the above gives
the complete set of true responses
E
Which of the following statements are true?
I The P-value of a test is the probability of
obtaining a result as extreme as the one
obtained assuming the null hypothesis is
true.
II If the P-value for a test is .043, the
probability that the null hypothesis is true
is .043.
III When the null hypothesis is rejected, it is
because it is not true.
(A) I only
(B) II only (C) III only
(D) I and III
(E) None of the above gives
the complete set of true responses
A
When leaving for school on an overcast
morning, you make a judgment on the null
hypothesis: The weather will remain dry.
What would the results be of Type I and II
errors?
(A) Type I error: get drenched. Type II error:
needlessly carry around an umbrella
(B) Type I error: needlessly carry around an umbrella.
Type II error: get drenched
(C) Type I error: carry an umbrella, and it rains. Type
II error: carry no umbrella, but weather remains
dry.
(D) Type I error: get drenched. Type II error: carry no
umbrella, but weather remains dry.
(E) Type I error: get drenched. Type II error: carry an
umbrella, and it rains.
B