Descriptive Statistics and Quantitative Comparisons

For questions 1-4, use the “Problem Set 2” file in the “Files” section on Canvas that consists of 2011 data from the Texas Transportation Institute (TTI) on urban mobility to complete the following questions. You may find you need to do some data compilation beforehand to enhance the readability of your answers. Questions 5-7 relate to the material in the Miller reading, while Z-scores in question 4 are covered in Miller too.

1. (20 points) Using the MEAN, MEDIAN, and MODE functions in Excel, calculate the mean, median, and mode for the variables “Population,” “Annual Hours of Delay per Auto Commuter,” “Condition of Public Transportation Service were Discontinued: Annual Delay Increase per Auto Commtuter (hours),” and “Presence of Urban Rail.” For each measure, state what the most representative measure(s) of central tendency are, and why, using the numerical properties of the variable to justify your answer.

1. (20 points) For the “Truck Commodity Value (\$mil) variable, calculate the standard deviation using only standard operators as well as the AVERAGE, SUM, and SQRT functions. Once you have done this verify your calculations by using the Analysis ToolPak to produce the Descriptive Statistics for these data. Make sure that you select “Summary Statistics” when you go to run the statistics. Correctly describe the central tendency and distribution from the results.

1. (20 points) Utilize the Analysis ToolPak to produce the Descriptive Statistics for the variables “Public Transportation: Annual Unlinked Passenger Trips (Million),” “Average State Gasoline Cost (\$/gallon),” “Excess CO2 Due to Congestion: Congested C02 Pounds (million), and Excess CO2 Due to Congestion: CO2 per Peak Auto Commuter (pounds). Make sure that you select “Summary Statistics” when you go to run the statistics. Then, use this information to assess whether or not the variables are normally distributed.

1. (20 points) The variable “Annual Effects of Operations Treatments: Delay Reduction (1000 hours)” measures the amount of delay vehicles experience in traffic that has been eliminated due to various strategies used to improve traffic and vehicle flow in cities. Use the “Standardize” function in Excel to calculate the Z-scores for each of the cities in the sample, based off of a population = 1,330,000 hours and SD = 1,372,000. Which 3 cities are saving the most hours of delay, and which three the least? Use table 5.3 in Miller to assist you in writing your answer.

1. (10 points) Identify the type of quantitative comparison used in each of the following statements.
1. “Yesterday, New York City received 5.5 inches of snow.”
2. “Ian Thorpe’s margin of victory in the 400-meter freestyle was 0.74 seconds.”
3. “A panel of independent tasters preferred new Wheat Whistles 3 to 1 over their regular snack.”
4. “The Dow Jones Industrial Average dropped 0.6% since this morning’s opening.”
5. “On sale, the scanner cost \$10 less than the suggested list price.”
6. “Cornstarch has twice the thickening power of flour; for each teaspoon of flour called for in a recipe, substitute on half teaspoon of cornstarch.”
7. “Median income for the metro region was \$31,750.”
8. “At 6’3″, Joe is two standard deviations taller than the average adult man.”
9. “Sixty-eight percent of registered voters turned out for the primary election.”
10. “State U was seeded first in the tournament.”

1. (10 points) Indicate whether each of the following statements is correct. If not, rewrite the second part of the sentence to agree with the first.
1. “Brand X lasts longer than Brand T, with an average lifetime 60% as long as Brand T’s.”
2. “Mean attendance at Root4 U increased 25% since last year, from 4,000 to 5,000 fans per game.”
3. “The ratio of flour to butter in shortbread is 2:1; it uses twice as much butter as flour.”
4. “At this time of year, reservoirs are usually 90% full. Currently, with reservoirs at 49% of capacity, water levels are only about 54% of normal.”
5. “Nadia’s test score was higher than 68% of students nationwide (Z = 1.0).

1. (10 points bonus) One thousand people lived in Bubbaville, TX in 2010 and the population was growing at an annual rate (r) of 2.0% per year.
 Year Population Increase from Previous Year Cumulative Increase since 2010 Percentage Change since 2010 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

1. Use the formula Pt = P0 × ert to fill the population for each year into the table. The year 2010 is year 0, t is the number of years since 2010, r (the annual growth rate, expressed as a proportion) is 0.02, and e is the base of the natural logarithms. You may make calculations in Excel if you prefer.
2. Calculate the increase in population from the preceding year for each year in the table. Write a sentence explaining the pattern of annual population increase across the 10-year period.
3. The cumulative increase is the total number of people added to the population since 2010. How many more people live in Bubbaville in 2020 than in 2010?
4. Calculate the percentage change relative to 2010 for each year. Write a sentence to describe the percentage change in population between 2010 and 2020.
5. What is the ratio of the population size for 2020 compared to 2010? How does that ratio relate to the percentage change over that 10-year period?
6. How do the annual rate of growth and the percentage change between 2010 and 2020 relate?

This is due by 11:59 pm on Sunday, February 27th, and is worth 100 points toward your final grade.

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