Question

Please write it seriously and clearly

2) Construct 95% Confidence Intervals for the PERCENTAGE of Aluminum ductility and Steel ductility. TREAT THE PERCENTAGE DATA AS REGULAR DATA VALUES, AND NOT AS PROPORTIONS AS I SUGGESTED EARLIER. What can you say about the typical proportion ductility for Aluminum with respect to Steel? From a statistically significant perspective, can you conclude the Aluminum ductility is greater than Steel ductility based upon these CIs?

Laboratory 1: Tensile Testing The tensile test can provide considerable information about the mechanical properties of a material. It involves deforming a uniform bar of material in uniaxial tension until failure while measuring the load and elongation. 18 groups of engineering students at Western University used a modern tensile testing machine during autumn 2017 to perform tensile tests on specimens made from a steel and an aluminum alloy to determine some material properties such as Ductility as reduction of area (%RA) at fracture The ductility of the tested tensile specimen can be measured using the percentage reduction in area at the necked portion of the specimen as Ao-A, %RA-Ductility x100 where A is the initial cross sectional area and A recorded results are presented in table 1 is the final (necked area). Their Lab 1: Ductilit Aluminum | 63.32% 48.40% 48.10% 49.54% 58% 68.78% 64% 43.57% 65.69% Steel Group1 Group2 Group3 Group4 Group5 Group6 Group Group8 Group9 36.28% 28.50% 56.25% 34.86% 37% 39.33% 13.26% 33.49% 22.02% Lab 1: Ductilit Aluminum | 62.85% 55.07% 62% 58.39% 57.80% 45.90% 63.08% 66.08% 63.51% Steel Group10 Group11 Group12 Group13 Group14 Group15 Group16 Group17 Group18 25.76% 34.93% 35% 31.60% 41.90% 35.90% 33.93% 38.93% 35% im The median is the same as the 50th percentile, because 50% of values fall below this value. Other percentiles for a data set can be identified to provide more information. The 0th (i.e. Min), 25th, 50th, 75th, and 100th (i.e. Max) percentiles are reported as the five-number summary. These values are more commonly called the minimum, 1st quartile, 2nd quartile, 3rd quartile, and maximum. The five-number summary is a useful measure of variation for skewed interval/ratio data or for ordinal data. 25% of values fall below the 1st quartile and 25% of values fall above the 3rd quartile. This leaves the middle 50% of values between the 1st and 3rd quartiles, giving a sense of the range of the middle half of the data. This range is called the interquartile range (IQR) Percentiles and quartiles are relatively robust, as they aren't affected much by a few extreme values. They are appropriate for both skewed and unskewed data. summary (tensile) Aluminum Steel Min. 43.57 1st Qu. 50.9 Median 60.20 Mean 58.00 3rd Qu. 63.46 Max 68.78 OR 12 13.26 32.07 4.97 34.11 36.82 2 4.75 describe (tensile) Aluminum Steel vars n mean sd median mad min max range skew kurtosis se 1.83 2 18 34.11 8.78 34.97 4.00 13.26 56.25 42.99 0.0 1.32 2.07 18 58.00 7.77 60.20 6.62 43.57 68.78 25.21 -0.5 1.26 0 1 2 > boxplot (tensile) Aluminum Steel

Answer 1

df =n-1 = 18-1 = 17

t = =t.inv.2t(0.05,17)

= 2.1098

for alumium ,

Xbar = 58 ,s = 7.77

95% confidence interval = (54.136,61.864)

for steel

xbar = 34.11 , sd = 8.78

95% confidence interval = (29.744,38.476)

we see that aluminum has confidence interval higher that that of steel

hence proportion ductility for Aluminum is high that that for steel