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Category Programming R | R Studio Graduate Solved Statistics Assignment

Assignment Description

Use R to solve the following problems: Chapter1: 13; 24; 29; 53; Chapter 4: 95 Chapter1:

13. Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article “Establishing Mechanical Property Allowables for Metals” (J. of Testing and Evaluation, 1998: 293–299) used the accompanying data on tensile ultimate strength (ksi) as a basis for addressing the difficulties in developing such a method.

122.2 124.2 124.3 125.6 126.3 126.5 126.5 127.2 127.3 127.5 127.9 128.6 128.8 129.0 129.2 129.4 129.6 130.2 130.4 130.8 131.3 131.4 131.4 131.5 131.6 131.6 131.8 131.8 132.3 132.4 132.4 132.5 132.5 132.5 132.5 132.6 132.7 132.9 133.0 133.1 133.1 133.1 133.1 133.2 133.2 133.2 133.3 133.3 133.5 133.5 133.5 133.8 133.9 134.0 134.0 134.0 134.0 134.1 134.2 134.3 134.4 134.4 134.6 134.7 134.7 134.7 134.8 134.8 134.8 134.9 134.9 135.2 135.2 135.2 135.3 135.3 135.4 135.5 135.5 135.6 135.6 135.7 135.8 135.8 135.8 135.8 135.8 135.9 135.9 135.9 135.9 136.0 136.0 136.1 136.2 136.2 136.3 136.4 136.4

136.6 136.8 136.9 136.9 137.0 137.1 137.2 137.6 137.6 137.8 137.8 137.8 137.9 137.9 138.2 138.2 138.3 138.3

138.4 138.4 138.4 138.5 138.5 138.6 138.7 138.7 139.0

139.1 139.5 139.6 139.8 139.8 140.0 140.0 140.7 140.7

140.9 140.9 141.2 141.4 141.5 141.6 142.9 143.4 143.5 143.6 143.8 143.8 143.9 144.1 144.5 144.5 147.7 147.7

24. The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal-width classes with boundaries 4000, 4200, . . . . [The histogram will agree with the one in “Comparison of Properties of Joints Prepared by Ultrasonic Welding and Other Means” (J. of Aircraft, 1983: 552–556).] Comment on its features.

5434 4948 4521 4570 4990 5702 5241 5112 5015 4659 4806 4637 5670 4381 4820 5043 4886 4599 5288 5299 4848 5378 5260 5055 5828 5218 4859 4780 5027 5008 4609 4772 5133 5095 4618 4848 5089 5518 5333 5164 5342 5069 4755 4925 5001 4803 4951 5679 5256 5207 5621 4918 5138 4786 4500 5461 5049 4974 4592 4173 5296 4965 5170 4740 5173 4568 5653 5078 4900 4968 5248 5245 4723 5275 5419 5205 4452 5227 5555 5388 5498 4681 5076 4774

4931 4493 5309 5582 4308 4823 4417 5364 5640 5069 5188 5764 5273 5042

5189 4986

29. Consider the following data on types of health complaint (J=joint swelling, F= fatigue, B= back pain, M= muscle weakness, C =coughing, N= nose running/irritation, O= other) made by tree planters. Obtain frequencies and relative frequencies for the various categories, and draw a histogram. (The data is consistent with percentages given in the article “Physiological Effects of Work

Stress and Pesticide Exposure in Tree Planting by British Columbia Silviculture Workers,” Ergonomics, 1993: 951–961.)

O O N J C F B B F O J O O M

O F F O O N O N J F J B O C

J O J J F N O B M O J M O B

O F J O O B N C O O O M B F

J O F N

53. A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of investments, whereas blended funds seek a balance between current income and growth. Here is data on the expense ratio (expenses  as a % of assets, from www.morningstar.com) for samples of 20 large-cap balanced funds and 20 large-cap growth funds (“large-cap” refers to the sizes of companies in which the funds invest; the population sizes are 825 and 762, respectively):

Bl

1.03 1.23 1.10 1.64 1.30

1.27 1.25 0.78 1.05 0.64

0.94 2.86 1.05 0.75 0.09

0.79 1.61 1.26 0.93 0.84

Gr

0.52 1.06 1.26 2.17 1.55

0.99 1.10 1.07 1.81 2.05

0.91 0.79 1.39 0.62 1.52

1.02 1.10 1.78 1.01 1.15

a.  Calculate and compare the values of 𝑥𝑥̅, 𝑥𝑥 and s for the two types of funds.

b.  Construct a comparative boxplot for the two types of funds, and comment on interesting features.

Chapter 4: 95

95. Use a statistical software package to construct a normal probability plot of the tensile ultimate-strength data given in Exercise 13 of Chapter 1 (above), and comment.

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