QUESTIONS

1. Do the following exercises using appropriate non-parametric tests. In each case, provide your answers as

properly written sentences indicating what your null and alternative hypotheses are, what R methods

you used to implement the statistical tests, what your p-values are, and the conclusions you drew.

Unless otherwise stated, assume the level of signicance is 0.05 ( = 0:05).

Keep your answers short. For example, you could just answer as follows: “A Mann-Whitney non-

parametric test was implemented in R using the wilcox.test(sample1, sample2, alternative=”two.sided”)

call to test the null hypothesis that men and women do not differ in the number of cups of coffee they

drink (the alternative hypothesis is that there is a difference). The p-value for the test is 0.012. Thus,

we reject the null and conclude that there is a difference in the amount of coffee consumed by men and

women. [30 marks]

a) An analyst has been gathering data on the performance of different equipment brands (A, B, C

and D). Performance equipment is measured by the number of hours of continuous operation before

a major breakdown occurs. Using the following data, test if the equipment brands have the same

performance.

A: 2600,2379,2614,1906,2050,2474,2593,2520,1694,2566

B: 2908,2767,2820,3004,2506,2895,2762,2719,2901,2588,2627,2404,3073,2195,3133,2560,2908,2674,2413,2751

C: 2133,2388,2213,2384,2231,2540,2485,2345,2356,2482,2098,2073,2391,2413

D: 2742,2821,2723,2465,2448,2491,2303,2212,2578,2634,2630

b) Yield observations for 3 crop varieties (A, B & C) are as follows:

Variety A: 914, 1048, 1351, 1353, 1275

Variety B: 1963, 2052, 2291, 1755, 1674, 2464

Variety C: 1095, 1811, 1869, 1472, 1143, 1638, 1703

Test if the three varieties have the same yields.

c) A clinic has the following information on white blood cell (WBC) counts (in billion cells per litre)

for a group of Caucasian men and Caucasian women that visited in a particular day.

Caucasian women: 5.54,5.78,5.89,5.84,6.93,2.43,4.53,3.93,6.05,4.41,6.5,4.29

Caucasian men: 7.76,8.74,8.26,6.64,7.02,5.24,3.8,7.96

Use the data to test if the two groups have the same WBC counts.

d) Suppose you have the following WBC count for a sample of 6 black men: 7.54,6.76,5.2,4.76,3.27,4.42

Test if there is a difference between the WBC counts for black and Caucasian men.

e) Would your approach to the above test change if you knew that the scientic literature shows that

total WBC counts are lower for black people? Would that knowledge change the way you set up

your hypothesis and conduct the statistical test? Explain. And if your answer is ‘yes’, do the test

again with the new setup (new null and alternative hypothesis). (There is an article included in

the folder on this topic that you can quickly skim through (Coates et al. 2020) to learn about the

type of WBCs that are lower in one race than another and about possible explanations. You can

check the medical dictionary here for basic information on WBC types and their functions.)

2. Use the data on human height described in the Appendix (C1) to do the following exercises. Read the

description of the data in before you proceed.[30 marks]

a) Summary of female height increases (15 marks)

Suppose our interest is in understanding the percent increases in adult female height between 1896

and 1996 and how these increases vary between continents. The following table presents summary

statistics on female height and its growth over the century, by continent and for the whole world.

The data shown in columns are: number of countries included from the continent (n); average adult

height for females born in 1996 (cm.1996); average percent increase (pct.mean); minimum increase

(pct.min); maximum increase (pct.max); standard deviation of the increase (pct.sd); and coefficient

of variation for the increase(pct.cv).

i) Examine the statistics in the table and summarise your observations about current female

height and its change between 1896 and 1996. Limit your answer to between 175 and 200

words. Answers that are longer or shorter will attract penalties.

ii) Write a script to generate in R a data frame with all the summary data shown in the table. The

script should start by reading in the le with height data and then proceed to calculate and

organise all the summary statistics. A stub is provided below for you as guidance on how you

could set up your script. The marker will copy and paste your script for evaluation. Therefore,

you should execute it to conrm that it works as intended.

R programming assignment, r programming expert , Assignment 2

SCIE4401,

University of Western Australia assignment, University of Western Australia expert writer

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