Computer based analysis, programming homework help

The following is a class homework. please show all work and assumptions. Answer all parts clearly

its a computer based analysis class for engineering students

Point values are shown in brackets. Show your work. Explain any assumptions you make.
1. [20] Preventing fatigue crack propagation in aircraft structures is an important element of
aircraft safety. An engineering study to investigate fatigue crack in n = 9 cyclically loaded wing
boxes reported the following crack lengths (in mm): 2.13, 2.96, 3.02, 1.82, 1.15, 1.37, 2.04, 2.47,
and 2.60. Calculate the sample average and sample standard deviation. Construct a dot diagram
of the data.
2. [10] Five observations are as follows: 20.25, 21.38, 22.75, 20.89, and 26.50. Suppose that the
last observation is erroneously recorded as 265.0. What effect does this data recording error have
on the sample mean and standard deviation? What effect does it have on the sample median?
3. [25] Eighteen measurements of the disbursement rate (in cm/sec) of a chemical disbursement
system are recorded and sorted:
6.50 6.77 6.91 7.38 7.64 7.74 7.90 7.91
8.21
8.26
8.30
8.31
8.42 8.53 8.55 9.04 9.33
9.36
(a) Compute the sample mean and sample variance.
(b) Find the sample upper and lower quartiles.
(c) Find the sample median.
(d) Construct a box plot of the data.
4. [20] Establishing the properties of materials is an important problem in identifying a suitable
substitute for biodegradable materials in the fast-food packaging industry. Consider the flowing
data on product density (g/cm”) and thermal conductivity K-factor (W/mK) published in
Materials Research and Innovation:
Thermal Conductivity, y 0.0480 0.0525 0.0540 0.0535 0.0570 0.0610
Product Density, x
0.1750 0.2200 0.2250 0.2260 0.2500 0.2765
(a) Create a scatter diagram of the data. What do you anticipate will be the sign of the sample
correlation coefficient?
(b) Compute and interpret the sample correlation coefficient.
5. [25] Consider the two samples shown here:
Sample 1: 20, 19, 18, 17, 18, 16, 20, 16
Sample 2: 20, 16, 20, 16, 18, 20, 18, 16
(a) Calculate the range for both samples. Would you conclude that both samples exhibit the same
variability? Explain.
(b) Calculate the sample standard deviations for both samples. Do these quantities indicate that
both samples have the same variability? Explain.
(c) Write a short statement contrasting the sample range versus the sample standard deviation as
a measure of variability.