*Please
consider using 1.5 spacing and/or wider margins so we have space for writing
comments. Include (both) names of
individuals who worked on the assignment in each file. If you are submitting
joining, you MUST join a HW 2 group first. Please use Word or PDF format
only. Remember to integrate your output
with your discussion. Points will be
deducted if you are missing output.*

**1) **Complete
the week 2 survey by Friday

**HW 3: **Complete
the water usage survey by Feb. 2

·
Water usage survey instructions: Keep a journal of your water
usage for 7 consecutive days. The
variables you will keep track of are

o
How many times did you shower

o
How long was each shower

o
How many baths did you take

o
How long do you leave your bathroom sink water running

o
Number of toliet flushes

o
How long do you leave your kitchen faucets running

o
Hand washing/dishwasher use

o
Car washes

o
Miles driven each day

After
the 7 days, open the water use survey
(you will need to make a copy first) and complete rows 2-15 (and indicate CA
for the state you live in). Be sure to make any conversions you need before
entering your values in column D (e.g., average per day, number per year).. Everyone will
leave rows 16-20 blank. When you have completed your journal, use the “Water
Survey” link in
Canvas to::

(a)
Upload a copy of your journal

(b)
Report your Total (Individual Daily Use) from cell F21.

Then
also answer:

(c)
Report any suspected data quality errors.

(d)
Suppose we find the average water usage (find the mean of all your answers to
b), will this be a parameter or a statistic?
Then define in words a corresponding statistic/parameter.

(e)
Suggest a research question you could explore using __one__ of these
variables.

**2)** Dogs have a keen sense of smell. They
are used for search and rescue, explosive detection, sniffing out illegal drugs
in luggage at airports, and locating game while hunting. Can they also tell
whether someone has COVID-19 by sniffing a specimen of sweat from a person? (example)
We will look at one study on Maika, a 3-year-old female Belgian Malinois whose
specialty is search and rescue. See Grandjean, Dominique, et al. Can
the detection dog alert on COVID-19 positive persons
by sniffing axillary sweat samples? A proof-of-concept study https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0243122

Maika completed 57
trials where she would sniff four different sweat specimens, one of which was
from a COVID positive person, and then sit in front of the specimen she
determined to be the positive specimen. In these 57 trials, Maika chose the
COVID positive specimen 47 times.

(a) Report the value of
the observed statistic.

(b) Define the
parameter of interest and use an appropriate symbol to refer to this unknown
value.

(c) State the null and
alternative hypotheses for Maika, in symbols and in words.

(d) Let *X* refer
to the number of correct identifications by Maika. If the null hypothesis is true, what
probability distribution does *X* follow? (Give the name of the
distribution, and define the inputs of the probability distribution)

(e) Use the One
Proportion Inference applet
(remember you can skip the simulation and go straight to the binomial) or R
(you can use one of the widgets in the text or if on your own, remember to load
use load(url("http://www.rossmanchance.com/iscam3/ISCAM.RData")) (or JMP) to calculate the
exact binomial p-value for this study.
Be sure to include your output and document how you found it.

(f) According to the
distribution you identified in (d), what are the expected value (mean) and
standard deviation of *X*, assuming the null hypothesis is true? Show your
work.

(g) Using your values
from (f), how many standard deviations is Maika’s result from the expected
number of successes assuming the null hypothesis is true? Do you consider this value to be convincing
evidence against the null hypothesis?
Justify your answer. Is your
answer consistent with (e)? Explain.

(h) Now calculate the
p-value for assessing whether there is convincing evidence that Maika’s
probability of successfully identifying the correct specimen is larger than
0.70. (Include your output.)

(i) How do the p-values
in (e) and (h) compare (which is larger)? Why?

(j) Calculate a
two-sided p-value to assess whether there is convincing evidence that Maika’s
probability of successfully identify the correct
specimen differs from 0.70. (Include your output.)

(k) How do the p-values
in (h) and (j) compare (which is larger)? Why?

(l) Using
trial-and-error find the *smallest* plausible value for the probability of
Maika correctly identifying the covid sample? (*Hint*: Use 0.05 as the
cut-off for deciding the p-value is small. Include justification. Use 3 decimal places.)

Dogs’ ability to sniff out disease has also been used for
many other diseases as well. Why do you think this method isn’t used more
regularly for disease diagnosis? (See this Ask Marilyn column https://parade.com/929476/marilynvossavant/how-well-can-dogs-detect-cancer/
)