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M12
L1
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correctness or
given by two
other classmates.
1) Eleven percent
of the products
produced by an
industrial process
over the past
several months
fail to conform to
1a) Proportion, p, of nonconforming items for the modified process.
1b) Use one proportion z-interval. The conditions to be met are:
 Not sure if random, but sample was chosen from population of interest. Results may not be generalizable
 N=300, so 300(10) = 3000. There is no indication given in the problem that there are at least 3000 parts made. It
is reasonable to assume it, though, so it is safe to use this standard deviation formula. Proceed with caution
 np ≥10?
300(.05) = 15 ≥ 10 , n(1-p) ≥ 10 300(1-.05) = 285 ≥ 10
So, the distribution of the sample proportion is approximately normal
1c) (.0424, .1176) Used formula for 1 prop z-interval
1d) I am 95% confident that the true proportion, p, of nonconforming items in the mfg process is between 4.24% and
11.76%
2) The best answer choice is “e” (more than one condition violated). The condition “n is so large that both the count of
successes np and the count of failures n(1 – p) are ten or more” is violated because 100(.07) is not greater than or equal
to 10. The condition “The data are an SRS from the population of interest” is also violated because the callers were
volunteers, thus random sampling measures were not used.
3) Using .33 as the sample proportion, and 0.06 as the margin of error (.12/2), and 1.645 for z* - the sample size is 167
patients
the specifications.
The company
modifies the
process in an
attempt to reduce
the rate of
nonconformities.
In a trial run, the
modified process
produces 16
nonconforming
items out of a total
of 300 produced.
You are to
construct a 95%
confidence
interval for the
proportion, p, of
nonconforming
items for the
modified process.
2) A radio talk
show host with a
large audience is
interested in the
proportion p of
listening area who
think the drinking
age should be
raised to 25. To
find this out he
poses the
following question
to his listeners.
“Do you think that
the drinking age
should be raised to
twenty-five in
light of the fact
that more and
more people
charged with
drunk driving are
between the ages
of 21 and 24?” He
phone in and vote
“yes” if they agree
the drinking age
should be raised
and “no” if not.
Of the 100 people
who phoned in 7
Which of the
following
conditions for
proportion using a
confidence
interval are
violated?
(a) The data are
an SRS from the
population of
interest.
(b) The
population is at
least ten times as
large as the
sample.
(c) n is so large
that both the count
of successes n(phat) and the count
of failures n(1 –
)p-hat)) are ten or
more.
(d) There appear
to be no
violations.
(e) More than one
condition is
violated.
NOTE: You must
explain why your
3) Some scientists
believe that a new
drug would
benefit about onethird of all people
with a certain
degenerative
nerve disease. To
estimate the
proportion of
patients who
would benefit
from taking the
drug, the scientists
to a random
sample of patients
who have the
disease. What
sample size is
needed so that the
90% confidence
interval will have
a width of 0.12?
Justify your
M12
L2
questions given,
then explain how
you obtained
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correctness or
given by two
other classmates.
1) In a large
1) “d” - There is significant evidence of a decrease in the proportion of freshmen who graduated in the bottom third of
their high school class that were admitted by the university. If you run the test the p-value is .0238
2) “b” = .15 The answer is obtained by .45 - .3 = .15
3) “e” none of the above. The correct standard deviation is 0.0526. This is obtained from the denominator in the formula
for the z-statistic for 2 proportion z-tests. P-hat is (X1 + X2)/(n1 + n2).
Midwestern
university (the
class of entering
freshmen being on
the order of 6000
or more students),
an SRS of 100
entering freshmen
in 1993 found that
20 finished in the
bottom third of
their high school
standards at the
university were
tightened in 1995.
In 1997 an SRS of
100 entering
freshmen found
that 10 finished in
the bottom third of
their high school
class. Let p1 and
p2 be the
proportion of all
entering freshmen
in 1993 and 1997,
respectively, who
bottom third of
their high school
class.
What conclusion
should we draw?
(a) We are 95%
confident that the
standards have
been tightened.
(b) Reject H0 at
the = 0.01
significance level.
(c) Fail to reject
H0 at the = 0.05
significance level.
(d) There is
significant
evidence of a
decrease in the
proportion of
freshmen who
bottom third of
their high school
class that were
university.
(e) If we reject H0
at the = .05
significance level
based on these
results, we have a
5% chance of
being wrong.
NOTE: you must
explain why your
2) An SRS of size
100 is taken from
a population
having proportion
0.45 successes.
An independent
SRS of size 400 is
taken from a
population having
proportion 0.30
successes. The
sampling
distribution of the
difference in
sample
proportions has
what mean?
(a) 0.3
(b) 0.15
(c) The smaller of
0.45 and 0.30
(d) The mean
cannot be
determined
without the
sampling results.
(e) None of the
above. The
_______________
______________.
NOTE: you must
explain why your
3) Using the
information you
have in problem
#2 above, find the
standard deviation
for the sampling
distribution for the
difference in
sample
proportions
(a) 1.3
(b) 0.40
(c) 0.047
(d) 0.0002
(e) None of the
above. The
_______________
______________.
M13
L1 ChiSq Dist
following
questions. After
you make your
post you'll be
able to see
TPOS 2nd
edition:
Work Problems
13.1, 13.3.
TPOS 3rd
edition:
Work problems
14.1, 14.5.
TPOS 2nd Edition:
13.1) This answer is in the back of your book
13.3) In back of book, but the answer below has more information:
H0: The tobacco plants fit our expected pattern of 1:2:1.
Ha: The tobacco plants do not fit our expected pattern of 1:2:1.
Our data are counts. We are evaluating all of the offspring, so our data
should be representative of such crosses described. (The observed
counts are in L1. The expected frequencies are in L2, and the expected
counts are in L3. To obtain the expected counts multiply the values in
L2 by the sum of L1.)
All expected counts are greater than 5.
with 2 degrees of freedom
In L4 we calculate the 2 contributions of each category.
We find (L1-L3)2/L3.
Fail to reject H0, a value this extreme may occur by chance alone more
than 6% of the time.
We lack strong evidence of a deviation from the expected pattern. We
do have some evidence and may wish to recommend that the
experiment be repeated with additional data, to be certain of the
significance, or lack thereof.
TPOS 3rd Edition:
#14.1) This answer is in the back of your book.
#14.5) This answer is the same as #13.3 above.
M13
L1
goodn
ess of
fit
following
questions. After
you make your
post you'll be
able to see
TPOS 2nd
edition:
Work Problems
13.11, 13.13
TPOS 3rd
edition:
Work Problems
14.10, 14.8
TPOS 2nd Edition:
#13.11)
Step 1:
H0: The Trix cereal flavors are uniformly distributed.
Ha: The Trix cereal flavors are not uniformly distributed.
Step 2:
Our data are counts. We are evaluating all of a box of cereal, and that
is our population. (We can consider the box to be a random sample of
all possible boxes of cereal, but in that case, it is a very small sample.)
(The observed counts are in L1. The expected frequencies are in L2,
and the expected counts are in L3. To obtain the expected counts
multiply the values in L2 by the sum of L1.) Note that since each flavor
is expected to be present in an equal amount, each one is expected to
be 20% of the total.
All expected counts are greater than 5.
Step 3:
with 4 degrees of freedom
In L4 we calculate the 2 contributions of each category. We
find
.
Step 4:
The scale doesn't really extend far enough to see the
shaded region beyond 47.
Step 5:
Step 6:
Reject H0, a value this extreme will rarely occur by chance alone.
Step 7:
We have strong evidence that the distribution of flavors in the box of
Trix cereal is not uniform. Examining the 2 contributions of each
category we see that the third (lime) is underrepresented and the fourth
(orange) is overrepresented. These are the largest of the 2
contributions.
#13.13)
Step 1:
H0: The distribution of Parts I through IV are uniform for a carnival
game wheel.
Ha: The distribution of Parts I through IV are not uniform for a
carnival game wheel.
Step 2:
Our data are counts. We are evaluating a random sample of spins of
this wheel. ( (The observed counts are in L1. The expected frequencies
are in L2, and the expected counts are in L3. To obtain the expected
counts multiply the values in L2 by the sum of L1.) Note that since
each part is expected to be present in an equal frequency, each one is
expected to be 25% of the total.
All expected counts are greater than 5.
Step 3:
with 3 degrees of freedom
In L4 we calculate the 2 contributions of each category. We
find
.
Step 4:
The scale doesn't really extend far enough to see the
shaded region beyond 24.
Step 5:
Step 6:
Reject H0, a value this extreme will occur less than 1% of the time by
chance alone.
Step 7:
We have strong evidence that the distribution of Parts I, II, III, and IV
is not uniform. Examination of the 2 contributions of each category we
see that the largest contribution is the overrepresentation of Part IV,
the circumstance where the player wins nothing. These results make
the wheel appear unbalanced.
TPOS 3rd Edition:
#14.10) This answer is the same as # 13.11 above
#14.8) We want to test Ho: p1 = p2 = p3 = ... = p12 versus Ha: at least one of the
proportions differs from 1/12. There were 2779 responses, so we should expect
2779/12 = 231.58 for each sign. The conditions for inference (231.58 > 5) is
satisfiied. The chi-squared test statistic is:
With a df 12 - 1 = 11, we find from Table D that the p-value is 0.20 < p < 0.25. Using
software the p-value is 0.212. There is not enough evidence to conclude that births
are not uniformly spread throughout the year.
M13
L2
Two
way
tables
following
questions. After
you make your
post you'll be
able to see
TPOS 2nd
edition:
TPOS 2nd Edition:
#13.15)
a) r = the number of rows in the table and c = the number of columns in the table
b)
Goal
Female
HSC-HM
0.21
Work Problems
13.15.
TPOS 3rd
edition:
Work problems
14.12.
HSC-LM
0.10
LSC-HM
0.31
LSC-LM
0.37
c) Hopefully by now you can create a bar graph that comepares the two genders. If not, then
write me or one of your fellow students for help. Remember that when we describe any
distribution of categorical data (i.e., a bar chart) then we must talk about what happens the
most, what happens the least, and any overall trend. Females participate in sports more than
males in the two categories of low social comparison and Males participate in sports more than
females in the two categories of high social comparison. Overall it appears that men and
women particpate in sports for different reasons.
d) Expected Counts:
Goal
Female
HSC-HM
22.5
HSC-LM
12.5
LSC-HM
.13
LSC-LM
19
e) For women, the observed counts are higher than expected for the two LSC categories and
lower than expected for the two HSC categories. For men, the observed counts are higher
than expected for the two HSC categories and lower than expected for the two LSC
categories. The comparison of the observed and expected counts shows the same association
we noticed with the proportions in parts (b) and (c).
TPOS 3rd Edition
14.12) This is the same problem as # 13.15 above.
M13
L2
indepe
ndenc
e
following
questions. After
you make your
post you'll be
able to see
TPOS 2nd
edition:
Work Problems
13.17 and 13.20.
TPOS 3rd
edition:
Work problems
14.17 and 14.22.
TPOS 2nd Edition:
13.17) This answer is in the back of the book
13.20)
(a) r=rows =3. c=columns = 2.
(b) When both parents smoke, 22.5% of students smoke.
(400/(9400+1380)=22.5%)
When one parent smokes, 18.6% of students smoke.
(416/(416+1823)= 18.6%)
When neither parent smokes, 13.9% of students smoke.
(188/(188+1168)=13.9%)
It looks like the student is more likely to smoke when one or
both parents smoke. The rate is highest when both parents
smoke.
(c)
(d) The null hypothesis states that the parents' smoking has no
effect on the students' smoking.
(e) To find the expected counts enter the data into matrix A and
run the 2 test. The recall matrix B to see the expected counts.
Expected Counts
Both parents
smoke
One parent smokes
Neither parent
smokes
Student smokes
Student does not
smoke
332.49
1447.51
418.22
253.29
1820.77
1102.71
(f) There are more than expected students who smoke when
both parents smoke, and fewer than expected who smoke when
neither parent smokes. We saw these same trends in the earlier
parts of this problem when we calculated the proportions of
student smokers for each category of parental smoking.
TPOS 3rd Edition:
#14.17) This answer is in the back of the book
#14.22) This is the same as #13.20 above
M13
L2
Indepn
dence
tests
(anoth
er one
M13
L2
indepe
ndenc
e part
2
No post required
following
questions. After
you make your
post you'll be
able to see
TPOS 2nd
edition:
Work problem
13.20 again, this
time making a 7step writeup.
TPOS 3rd
edition:
Work problems
14.22 again, this
time making a 7step writeup.
TPOS 2nd Edition:
13.20) 7-step writeup
Step 1:
H0: Student smoking is independent of parental smoking behavior.
Ha: Student smoking is not independent of parental smoking behavior.
Step 2:
Our data are counts. We are uncertain that our sample is a random one.
The expected counts are in Matrix B. All are greater
than 5.
Step 3:
with 2 degrees of freedom
Step 4:
The scale doesn't really extend far enough to see the
shaded region beyond 37.
Step 5:
Step 6:
Reject H0, a value this extreme will rarely occur by chance alone.
Step 7:
We have strong evidence that the smoking behavior by students is not
independent of the parents' smoking behavior.
TPOS 3rd Edition:
#14.22) This is the same as #13.20 above
M13
L3
no post required
homog
eneity
M14
L1
questions given,
then explain how
you obtained
Post your
Forum. Note that
this time the
“correct”
included. The
purpose of this
exercise is to see
how well you do
with this concept.
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clicking on
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be able to see
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correctness or
given by two
other classmates.
1. Which of
the
following
is NOT
one of
the basic
assumpti
ons that
must be
satisfied in
order to perform
inference for
regression of y on
x?
a) For each
value of x, the
corresponding
population of yvalues is normally
distributed.
b) The standard
deviation σ of the
population of yvalues
corresponding to a
particular value of
x is always the
same regardless of
the specific value
of x.
c) The sample
size (the number
of paired
observations (x, y)
in the sample
data) exceeds 30.
d) There exists a
straight line y = α
+ β x such that
for each value of
x, the mean µy of
the corresponding
population of yvalues lies on that
straight line.
2. If the
assumptions for
regression
inference are met,
then a normal
probability plot of
the residuals
should be
(a) Bell
shaped
(b) A group
of randomly
scattered points
(c) Roughly
linear
(d) Clearly
curved
3. If a test of
hypotheses rejects
H0: β= 0 in favor
of the alternative
hypothesis Ha: β >
0, where β is the
population
regression slope,
then the leastsquares regression
line
(a) Slopes
downward and to
the right when
plotted on the
scatterplot of
paired
observations (x, y)
(b) Is
useful for
predicting y given
x (within the
limits of x-values
covered by the
data)
(c) Can
be extrapolated
beyond the limits
of the x-values
covered by the
data to predict y at
any possible x
(d) Is not
useful for
predicting y given
x
4. Inference for
regression on the
population
regression slope β
is based on which
of the following
distributions?
(a) The t
distribution with n
– 1 degrees of
freedom
(b) The
standard normal
distribution
(c) The chisquare distribution
with n – 1 degrees
of freedom
(d) The t
distribution with n
– 2 degrees of
freedom
5. Suppose that
inference for
regression is
conducted on the
following small
data set:
x 12 14
16 18
y 2
3
5
6
The number
of degrees of
freedom for our
test statistic is
(a) 4
(b) 3
(c) 2
(d)
Inference cannot
be conducted on
this data set
because it is too
small.
(e) The
determined from
the information
given.
6. In inference for
regression, the
statistic s
represents
(a) The
estimate of the
standard deviation
s in the regression
model
(b) The
standard deviation
of the x-values in
the paired
observations (x, y)
(c) The
estimate of the yintercept
(d) The
standard deviation
of the y-values in
the paired
observations (x, y)
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