ST314 Data Analysis #1 | Complete Solution

Part I. (15 Points)
A study was done of the strength of high-performance concrete obtained by using superplastiziers and certain binders.  In particular, the following data was gathered on the flexural strength (a measure of the ability to resist failure in bending), which are measured in megapascals (MPa), for a sample of 29 beams made of high-performance concrete.

5.4    7.2    7.3    6.3    8.2    6.9    7.0    7.6    6.8    6.4    8.3    6.3    7.9    9    8.2
8.7    7.8    9.7    8.5    7.7    9.7    7.8    7.7    11.3    10.3    11.8    10.7    13.7    14.1    

In a short paragraph include the following:
a.    (3 points) Construct a stem-leaf display for these data by hand or using software.  
b.    (3 points) Calculate the descriptive statistics mean, median, standard deviation, lower 4th, upper 4th and fourth spread. (Can be displayed in a table).
c.    (3 points) Discuss the distribution of the flexural strength of these beams made of high-performance concrete (i.e. symmetric, skewed, unimodal, outliers etc...) include general statements about the range and significant features of the distribution.
d.     (2 points) Considering the shape of the data, which location measurement makes the most sense to use (mean or median)?  Explain your answer.
e.    (4 points) Suppose that specifications state that the flexural strength of a beam must be 7.0 MPa or higher if it is to be used as a support beam on a bridge.  What proportion of the beams in this sample would meet specifications? Based on this information, in your opinion do you feel these beams should be used as bridge supports?

Part II. (15 Points) Each year the EPA does an analysis on the current models of vehicles sold in the United States. The data provided in the data set EpaFE2016Data.csv is a subset of this analysis, if you are curious you may access the full data set from the EPA website http://www.fueleconomy.gov/feg/download.shtml.

Using the data set EpaFE2016Data.csv obtain descriptive statistics and graphical displays for the variable Estimated Fuel Cost.
a.    (4 points) Include (copy and paste) the stemplot, histogram and boxplot. Which do you feel best summarizes the data and why?
b.    (1 point) Is the stem plot a reasonable visual display for this data? Why or why not?
c.    (3 points) Give a table that includes the mean, median, standard deviation, 1st quartile, 3rd quartile and interquartile range.
d.    (4 points) Use a and b to thoroughly describe the data in the context of the problem. Include the shape, center and spread in your description.
e.    (3 points)Given the shape of the data which measure, the mean, median or either, would be a more appropriate to represent the center of the data? Explain your reasoning.   

Part III. (10 Points) The National Highway System Designation Act was signed into law in the Unites States on November 28, 1995. Among other things, the act abolished the federal mandate of 55 mile per hour maximum speed limits on roads in the United States and permitted states to establish their own limits. Of the 50 states (plus District of Columbia), 32 increased their speed limits either at the beginning of 1996 or sometime during 1996. Shown below are the percentage changes (increase or decrease in percentage) in interstate highway traffic fatalities from 1995 to 1996.
Data from “Report to Congress: The Effect of Increased Speed Limits in the Post NMSL Era,” National Highway Traffic Safety Administration, February, 1998)

States that retained 55 mph. limit in 1996
% change in fatalities    -29.1    -4.3    -80.5    -25.2    -12.9    3.4    -5.5    32.1    -9.1    42.4
    -14.3    10.8    -20    44.1    -9.7    -50    -16.4    -41.2    23.2    

States that increased speed limit in 1996
% change in fatalities    22.3    3.9    14.4    9.6    33.4    -31.2    33.5    17.8    -7.1    34.1    1.6
    24.5    41.3    -19.1    8.2    -17.9    9.4    41.4    -13.3    -1.8    3.4    18.2
    0    4.4    30    32.1    -7.9    17.9    50.7    17.9    62.5    5.4    

    
a.    (3 points) Calculate summary statistics (mean, median, standard deviation, IQR) for both groups.  
b.    (3 points) Using either plot describe the distributions of both groups. Include description of the shape, center, spread and outliers. Compare the two distributions in the context of the situation.
c.    (2 points) The histograms and side by side box plot display the same data, what are the advantages and disadvantages of each display? Specifically, what features are easier to see in each plot? Which plot do you prefer when comparing the two groups (No wrong answer)?
d.    (2 points) Given the data and visual displays, is there evidence that may support the claim that increasing the speed limit on interstate highways in associated with an increase in fatality rate? Explain.