代写WMEE14000、数据分析和统计方法代写、csv/R编程代写、代做C/C++设计报告

日期：2018-10-05 09:55

Problem Set 3

Data Analysis and Statistical Methods (WMEE14000 – 2018/2019)

Question 1

The Universal Declaration of Human Rights, article 11, states: "Everyone charged with a penal offence has the right to be presumed innocent until proved guilty…”. Suppose you are a judge in a statistics court and you must make one of the following decisions: either convict a defendant or to not convict the defendant.

a.How would you formulate the null and alternative hypotheses regarding guiltiness or innocence of the defendant, and why? [0.5 pt]

b.Explain the meaning of the risks of committing either a Type I or Type II error in this example. [0.25 pt]

c.How can you define power of this statistics court? [0.25 pt]

Question 2

The Calculus exam has been traditionally perceived as a difficult exam in the University of Lazyland (UoL) and the average grades was 6.5 out of 10. This year, one hundred students took the calculus exam, and the average and standard deviation of their grades were 6.41 and 1.65, respectively. The grades are listed in file “Q2.csv”.  After the exam, many students complained that the exam was more difficult than it used to be before and referred to the average grade (6.41<6.5) as an evidence. Suppose you are the advisor of examination committee of UoL and you intend to evaluate the claim of students:

a.How do you formulate the hypotheses for testing the claim? [0.5 pt]

b.Design an appropriate test statistic and explain whether you accept or do not accept the claim (with 95% confidence). [1 pt]

c.What the p-value and explain its meaning in this example. [0.5 pt]

d.In R, plot the t distribution curve of the test with horizontal lines (with labels) indicating the position of the statistic and the critical values, and with shaded rejection region. [0.5 pt]

Question 3

A program to help Alzheimer's patients remember the order of daily tasks use two methods: 1) using visuals, and 2) using visuals and intense verbal rehearsal. The table below illustrates the number of words remembered following the program, where the first methods is taught to Group 1 and the second methods is taught to Group 2 (The data can be found in “Q3.csv” as well).

Group 1Group 2

755534

347423

361452

2109547

3102546

855762

812878

5112879

8415957

534866

a.In R, design a run a test to check whether the variance of data in two groups are the same (at 95% confidence level), and draw your conclusion. [1 pt]

b.Design and conduct the test in part a without R. Find and type appropriate statistic, critical values, etc. [1 pt]

c.In R, design and run a test to check whether the methods taught to groups 1 and 2 have different effect, i.e. whether the mean number of word remembered by each groups differ. Explain item by item the output of test in R and draw your conclusion. [1.5 pt]

d.In R, run the test again with wrong assumption about the variance of groups and compare the results with part a. [0.5 pt]

e.By hand, conduct the test in part c. Find and type appropriate statistic, critical values, etc. [1 pt]

Question 4

A company wants to know whether a particular treatment reduces the amount of bacteria in milk. To find out, counts of bacteria were made on test samples before and after the treatment is applied resulting in the outcomes shown in table below. For instance, in the first sample, the bacteria count per ml milk before treatment is X11 = 6.98, after the treatment it is X12 = 6.95 (The data can be found in “Q4.csv”)

Bacteria counts per ml milk before and after treatment

SampleBeforeAfter

16.986.95

27.086.94

38.347.17

45.305.15

56.266.28

66.776.81

77.036.59

85.565.34

95.975.98

106.646.51

117.036.84

127.696.99

a.With the data above, what kind of statistical test is appropriate to check whether the treatment reduced the count of bacteria in milk. Explain why you chose such test and mention your main assumptions. [0.25 pt]

b.Design and run the test you chose in part a and draw your conclusion (at confidence level 95%). [0.75 pt]

c.The company researchers removed the “Sample” column to reduce size of their database. In addition, because of technical problems, the names of columns “Before” and “After” changed to “B” and “A”, respectively. Reviewer of a journal rejected their research article commenting that their statistical inference was wrong. Guess what could happened, design and run a test which was used by the reviewer, and advise the researchers to revise their article. [0.5 pt]