Transcribed Text
1.
Boxes cerval net weight ounces The veights
assumed normally distributed. new cereal ispurchased andwe
wishtol thato average. puts Aleast correct amount ofecreal boxes We
randomly select 6 boxes, and find they have weights with sample mean 8.10
sample standard deviation 20ounces.
(a) Suppose your data included all the box weights How would you check the normal
distribution Explain what would indicate violation this as
sumption (Note: You not have perform the check the given data.
(b) Perform test hypothesis that the average net weight of cereal
produced by hinei Sounces against the alternative that
greater than Sounces Test level a 0.05 (Clearly define paramete you're
estimating and the hypotheses you retesting, and give full and
2.
Totest whether friend's Googly powers. display two
windows entered either "Left' "Right depending which way Googly facing Then
the random number generator selected either left window, withprobability
0.5 for which display star. Let probability Googly guesses correctly
given
(assume
this
sonstant
In 80
trials
correctly
guessed
window
withthe
star Itimes
(a) Using nathematical notation, write down and alternative hypotheses for one
sided test.
(b) If the test statistic the number guesses trials, write down codeto
find the
Pvalue ofs
onesided test
(c) Even without that Googly's success rate sexpected ralue
under "value State your about
fish's
psychic
powers.
(d)
Continued from (b). Ifyou only that the code dbinom(40, 80, 0.5) gives
nember 0889. how would exact Pvalue (thetest (Hint: usethe
property of a symmetric probabilty distribution.)
3.
The file snoqualmie14 txt contains the daily precipitation (in Snoqualmie Falls,
WA fora random 365 days. After oyour computer you canload it
intol entering the command:
rainfall scan(file .choose())
d then seleeting
(a) Show that data does not come from normally distributed population Include
graph support your answer
(b) The mean annual rainfall Seattle is 37. inches per year. Test (at level 0.05) the
hypothesis mean rainiall Snoqualmi Falls different from mean rainfall
in
Seattle. (Clearly and the hypotheses you're
testing. and gives full and onclusion)
4.
ome year the United States, 4.217 million babies were born Of these, 2,173 million were
male and 2.074 million were female. With very few exceptions (e.g. identical twins). sexes
of the bables indepen we can binomial distributio model number
of pabies that female. Let p be the probability that random (future) newborn female.
(a) What percentage of the bables were female? (To get credit for this question you
must
give your answer percentage and you must round appropriately.)
(b) Suppose wish test the null hypothesis that the probability baby is female
is
50% Write down null and alternative hypotheses in mathematical this
test.
(c) Find the Pvalue. using both Binomial probability and Normal ap
proximation (Carefully show your work and R eodes.)
(d) Using the Central Limit Theorem find 95% onfidence interval forthe probability
that
abirthis female.
(e) Explain what thisconfidence interva means without using the word "confident."
(f) The Pvalue your test part isbasicall zero Fromt confidence
interval,
write
sentence
your
conclusion
abou
the
probability
that
random
new
is female
5.
The basketball pinyer Steph Curry sometimes shoots free throws with his mouthguard n his
mouth shoots throws with his mouthguard outside ( his mouth. His free
throw
statistics
for
one
season
were:
Free throws with mouthguard in: 110 completed 13 missed (89 4%)
Free throws with mouthguard out 198 completed 16 missed (92.5%)
His observed free throw completion rate was slightly higher wher his was outside
his mouth However we should check whether the difference could be plausibly explained as
luck
(a) Using Central Limit Theorem, find an approximate 95% forthe
probability that Curry completes free throw Give
numerical answer.
(b) Using Central Limit Theorem find approximate 95% confidence interva forthe
probability
that
Curry
completes
throw
out.
(c) Suppose wish test hypothesis Curry's probability completing
free
throw
sthe
same
with
mouthguard
with
mouthguard
out.
The
Pvalue for such test 0.33. What does this Pvalue tell you? Explain.
6. Rosene (1950) studied how quickly hairs on radish roots absorbed water when they were
immersed For each eleven radishes, measured the rate water for young
root hair and old root hair that radish. The data given below.
Radish
Table Radish root hair absorption data. Rates are cubic microns per square micron per
minute
For each pair. the "Young" number bigger than the FOld" number even without
test
it's clear that young roots take water more quickly. But how much more quickly?
(a) Explain what test should consider based the data and context and
why
(Hint:
1sample
2sample
test,
ztest
offtest
(b) Usea normal ploto differences (old minus young) and the mole sizeto
explain
hesitant
do such
atest
(the
one
you
proposed
nthe
previous
question
these
minus
young).
(c) Explain why we should not take the logs these diflerences minus young.)
(d)
Instead
fusing
we can
look
young.
This
ratio
looks come from amuch closer normal distribution Write codeto 90%
confidence interval the average value ratio.
7.
The basketball player Stephen Curry was the Most Valuable Plaver for the 2015 16
season Hei known being (throwine the basketball into the hoop)
long
distance.
Data
Canvas
ontains
the shots during the 2015 or these shots, sos them were
uccessful. data randor independent samples
(this isn't quite true
The variables
distance:
from
the
venue: "Home" was (in Oakland). "Away" if it was
somewhere
.
nade:
Load
the
currydist
read
txt".
currydist
read
Then von can extract variables frame using the dollar sign.
e.g. for the distance that R h casesensitive.)
(a) Create two R: one containing distances for Curry's shots home and
one containing the distances for Curry's Remember that we usesquare
brackets
for subsetting !

Draw
graph
that
compares
the
full
distributions
of
these
variables
and
describe your (Note: Boxplots distributions.
By "distribution" the PDF CDF. You should make visually nivvions which
distribution
(b)
show
that
the
d'stance
Curry's
shots
different from the distance o: furry shots awny7
Perform appropriate interval
Clearly
parameter
and
hypotheses
testing.
and
give
(Le.
"Reject"
"Don't
(c)
Show
that
the
met
or,1
they
why
they
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