### Due midnight, Friday, Jan. 19

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::

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

(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