Math 181B, Spring 2021, HW
math代做 | 代写report – 这个题目属于一个math的代写任务, 是有一定代表意义的math等代写方向
Clearly and thoroughly write your solutions on blank paper. Show all your work. You may list answers in exact form (e.g.,) or round to three decimal places (e.g., 3.142), unless the problem says otherwise. On any problem involving R, you should include your code and output as part of your answer. You may take a screenshot of the code/output, or write it by hand.
- Suppose you and two friends spent the entire COVID-19 quarantine working out at the gym in your residence. Its time to decide who, on average, is the strongest, so you take a series of exercises that everyone has been doing and record peoples one-rep max (the most a person can lift in a single repetition) for each in pounds. Below are the data:
You Friend 1 Friend 2
Bench Press 145 120 190
Squat 220 240 150
Deadlift 185 200 130
Shoulder Press 90 60 110
Barbell Biceps Curl 70 55 90
a. Explain why blocking is appropriate, define parameters, and write hypotheses for the issue you
want to resolve.
b. Calculate all parts of the RBD printout using only a simple calculator (exceptP-values, for which
you can use R). Then, write some R code to generate the RBD printout and check your answer.
Finally, make a decision about the hypotheses in part a using= 0.05.
c. After doing the analysis above, it seems like the exercises we choose have an important impact
on the analysis. Define parameters and write hypotheses that express this idea, and then use the
RBD printout to decide this issue using= 0.05.
d. Suppose you wanted to run a contrast study comparing the average amount lifted in lower-body
vs. upper-body exercises. Using the parameters from part c, write hypotheses for this setting.
(You should not try to run the analysis because we have a new situation that we havent dealt
with yet: A contrast study within an RBD! You may need to Google these exercises if you dont
spend much time in the gym.)
- Theres a reason I spend 100+ hours writing problems for my students in each class each quarter: Most problems in standard textbooks are as boring as watching paint dry. As an example, consider this actual problem setting about paint from a prominent mathematical statistics text: Researchers wondered if the amount of surface area (called coverage area, in ft^2 ) one gallon of paint can cover changes based on the type of paint or the type of roller used to apply the paint (yawn!). They ran some experiments and got these results:
Roller Brand 1 Brand 2 Brand 3
Paint Brand A 454 446 451
Brand B 446 444 447
Brand C 439 442 444
Brand D 444 437 443
a. Use R to create the RBD printout for this setting. Define parameters, state hypotheses, and use
the readout to decide if paint brand or if roller brand affect the average coverage using= 0.05.
b. Lets spice things up. Recreate the RBD printout, but first subtract the value 400 from each
coverage value in the data table. What do you notice? Form a conjecture and prove it using the
RBD computing formulas.
- Non-parametric statistics: Hipster edition! Youve just graduated and landed a statistics job at a new San Fran start-up that creates designer shampoos for men. The company has asked you to prove our shampoo is better than our competitors, so you design the following experiment: Youll take 13 random guys and shampoo the left side of their hair using your product and the right side with the leading competitors shampoo. Then, youll ask an official tester (blinded to the study) to rate each side on a 0 to 10 awesomeness scale. Below are the scores, recorded as: (left side score with new product, right side score with competitors product):
(7. 3 ,6),(9,10),(1, 2 .4),(3. 3 , 3 .2),(4. 5 , 4 .5),(7,4),(8,6),(9,5),(2. 1 , 3 .1),(2. 71 ,1),(10,9),(9. 3 , 2 .3),(5, 6 .5)
a. Discuss two things that bother you about the statement prove our shampoo is better than our
competitors.
b. Explain why a non-parametric test might make sense in this setting, whereas a parametric test
might be problematic.
c. Define a parameter of interest, state hypotheses, and conduct both an approximate and exact
sign test with= 0.05 to decide what to report to your boss.
- Here, we explore the signed rank sum statistic,T+, in data sets where rank tiesdo not occur.
a. Without using R, findP(T+= 10) for a data set withn= 8. Show all your work. Afterward,
write a single line of code in R that checks your answer.
b. Explain why, for anyn, the pmf ofT+must be symmetric. To do this, you need to provide an
argument for whyP(T+= 0) =P
(
T+=n(n 2 +1)
)
, andP(T+= 1) =P
(
T+=n(n 2 +1) 1
)
, and
in general,P(T+=t) =P
(
T+=n(n 2 +1)t