# Math 533, Applied Managerial Statistics Assignment 2016

August 31, 2017

Question
DATA DESCRIPTION PROBLEMS

Set 1 – Describing Qualitative Data Graphically

1.1 Diamonds are categorized according to the “four C’s”: carats, clarity, color and cut. Each diamond stone that is sold in the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted fromSingapore’s Business Times and saved in the DIAMONDS file. Color is classified as D, E, F, G, H, or I while clarity is classified as IF, V, VVS1, VVS2, VS1, or VS2.

a. Use a graphical technique to summarize the color and clarity of the diamonds. What is the color and clarity that occurs most often? Least often?

2.1 Owing to several major ocean oils spills by tank vessels, Congress passed the 1990 Oil Pollution Acts, which requires all tankers to be designed with thicker hulls. Further improvements in the structural design of a tank vessel have been implemented since then, each with the objective of decreasing the amount of outflow in the event of hull puncture. To aid in this development, the spillage amount and cause of puncture for 50 recent major oil spills from tankers and carriers has been reported. The data is in the file OILSPILL.

a. Use a graphical method to describe the cause of spillage for the 50 tankers (note: cause is classified as collision (C), fire/explosion (FE), hull fracture (HF), grounding (G), or unknown (U)).

b. Does the graph, part a, suggest that any one cause is more likely to occur than any other?

Set 2 – Describing Quantitative Data Graphically

1.2 Diamonds are categorized according to the “four C’s”: carats, clarity, color and cut. Each diamond stone that is sold in the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted fromSingapore’s Business Times and saved in the DIAMONDS file. Color is classified as D, E, F, G, H, or I while clarity is classified as IF, V, VVS1, VVS2, VS1, or VS2.

a. Use an appropriate histogram to describe the carat distribution of the diamonds.

b. Use an appropriate histogram to describe the carat distribution of diamonds certified by the GIA group.

c. Repeat part b for the HRD and IGI certification groups.

d. Compare the three carat distributions, parts b and c. Is there any particular certification group that appears to be assessing diamonds with higher carats than the others?

2.2 In order to estimate how long it will take to produce a particular product, a manufacturer will study the relationships between production time per unit and the number of units that have been produced. The line or curve characterizing this relationship is called alearning curve. Twenty five employees, all of whom were producing the same production task for the tenth time were observed. Each person’s task completion time was recorded. The same employees were observed again the 30th time they performed the same task and the 50th time they performed the task. The resulting times are contained in the file COMPTIME.

a. Construct an appropriate histogram for each of the three data sets.

b. Compare the above histograms. Does it appear that the relationship between task completion and the number of times a task is performed is in agreement with the observations noted above about production processes in general? Why?

3.2 Educators are constantly evaluating the efficacy of public schools in the education and training of American students. One quantitative assessment of change over time is the difference in scores on the SAT, which has been used for decades by colleges and universities as one criterion for admissions. The file SATSCORES contains the average SAT scores for each of the 50 states and the District of Columbia for the years 1990 and 2000.

a. Use appropriate histograms to display the two SAT score distributions. How have they changed over the last decade?

b. As another method of comparing the 1990 and 2000 SAT scores, compute thepaired differenceby subtracting the 1990 score from the 2000 score for each state. Summarize these differences by an appropriate histogram.

c. How do your conclusions for part a compare to those for part b?

4.2 For the data in the file DIAMONDS, construct a scatterplot for the data, with the number of carats on the horizontal axis and the price on the vertical axis. What type of trend do you detect?

Set 3 – Describing Quantitative Data Quantitatively

1.3 In order to estimate how long it will take to produce a particular product, a manufacturer will study the relationships between production time per unit and the number of units that have been produced. The line or curve characterizing this relationship is called alearning curve. Twenty five employees, all of whom were producing the same production task for the tenth time were observed. Each person’s task completion time was recorded. The same employees were observed again the 30th time they performed the same task and the 50th time they performed the task. The resulting times are contained in the file COMPTIME.

a. Obtain appropriate descriptive statistics for the distribution of times.

b. Compare the above results. Does it appear that the relationship between task completion and the number of times a task is performed is in agreement with the observations noted above about production processes in general? Why?

2.3 Educators are constantly evaluating the efficacy of public schools in the education and training of American students. One quantitative assessment of change over time is the difference in scores on the SAT, which has been used for decades by colleges and universities as one criterion for admissions. The file SATSCORES contains the average SAT scores for each of the 50 states and the District of Columbia for the years 1990 and 2000.

c. Obtain appropriate descriptive statistics to display the two SAT score distributions. How have they changed over the last decade?

d. As another method of comparing the 1990 and 2000 SAT scores, compute thepaired differenceby subtracting the 1990 score from the 2000 score for each state. Summarize these differences by using appropriate descriptive statistics.

e. How do your conclusions for part a compare to those for part b?

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