31 Jan Construct a stem-and-leaf displa

GES 255 – 002 Homework #1 Engineering Statistics I Spring 2020 Due Friday, January 24, 2020 Prof. Minjae Shin

1. The accompanying specific gravity values for various wood types used in construction appeared in the article “Bolted Connection Design Values Based on European Yield Model” (J. of Structural Engr., 1993: 2169–2186):

.31 .35 .36 .36 .37 .38 .40 .40 .40 .41 .41 .42 .42 .42 .42 .42 .43 .44 .45 .46 .46 .47 .48 .48 .48 .51 .54 .54

.55 .58 .62 .66 .66 .67 .68 .75

Construct a stem-and-leaf display using repeated stems, and comment on any interesting features of the display.

2. The accompanying summary data on particle sizes (nm) under certain experimental conditions was read from a graph in the article “Nanoceria—Energetics of Surfaces, Interfaces and Water Adsorption” (J. of the Amer. Ceramic Soc., 2011: 3992–3999):

(a) What proportion of the observations are less than 5?

(b) What proportion of the observations are at least 6?

(c) Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular, does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed?

(d) Construct a histogram with density on the vertical axis and compare to the histogram in (c).

3. The May 1, 2009, issue of The Montclarian reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (s of $): 590 815 575 608 350 1285 408 540 555 679

2

(a) Calculate and interpret the sample mean and median. (b) Suppose the observation had been 985 rather than 1285. How would the mean and median change?

4. The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft: .736 .863 .865 .913 .915 .937 .983 1.007 1.011 1.064 1.109 1.132 1.140 1.153 1.253 1.394 (a) Compute and compare the values of the sample mean and median. (b) By how much could the largest sample observation be decreased without affecting the value of the median?

5. The value of Young’s modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations: 116.4 115.9 114.6 115.2 115.8 (a) Calculate and the deviations from the mean. (b) Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation. (c) Calculate by using the computational formula for the numerator (d) Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance of these transformed values, and compare it to for the original data.

6. A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information:

(a) Are there any outliers in the sample? Any extreme outliers? (b)